We study the one-band Hubbard model on the trellis lattice, a two-dimensional frustrated lattice ... more We study the one-band Hubbard model on the trellis lattice, a two-dimensional frustrated lattice of coupled two-leg ladders, with hopping amplitude t within ladders and t between ladders. For large U/t this is a model for the cuprate Sr14-xCaxCu24O41. We investigate the phase diagram as a function of doping for U = 10t using two quantum cluster methods: The variational cluster approximation (VCA), with clusters of sizes 8 and 12, and Cellular dynamical mean field theory (CDMFT), both at zero temperature. Both methods predict a superconducting dome, ending at roughly 20% doping in VCA and 15% in CDMFT. In VCA, the superconducting order parameter is complex in a range of doping centered around 10%, corresponding to bulk chiral, T -violating superconductivity. However, the CDMFT solution is not chiral. We find evidence for a migration of the Cooper pairs from the inter-ladder region towards the plaquettes as doping is increased.
The onset of the pseudogap in high-T c superconducting cuprates (HTSC) is marked by the T * line ... more The onset of the pseudogap in high-T c superconducting cuprates (HTSC) is marked by the T * line in the doping-temperature phase diagram, which ends at a point p * at zero temperature within the superconducting dome. Although various theoretical and experimental studies indicate a competition between the pseudogap and superconductivity, there is no general consensus on the effects of the pseudogap within the superconducting phase. We use cluster dynamical mean field theory on a three-band Hubbard model for the HTSC to study the superconducting phase at T = 0, obtained when doping the charge-transfer insulator, for several values of U. We observe a first-order transition within the superconducting phase, which separates the underdoped and overdoped solutions. The transition to the underdoped solution is marked by a discontinuous increase in the spectral gap, and on further underdoping the spectral gap increases while the superconducting order parameter decreases. We conclude that this is due to the onset of the pseudogap in the underdoped region, which contributes to the increasing spectral gap; this is further consistent with the appearance of a pole in the normal component of the self-energy, in the antinodal region, in the underdoped solution. This is accompanied by a change in the source of the condensation energy from potential energy, in the overdoped region, to kinetic energy in the underdoped region. Further, we also observe that the d-wave node vanishes smoothly within the superconducting phase at low values of hole doping, within the underdoped region. We see this as a manifestation of Mott physics operating at very low doping. Various aspects of the results and their implications are discussed.
In the Cellular Dynamical Mean Field Theory (CDMFT), a strongly correlated system is represented ... more In the Cellular Dynamical Mean Field Theory (CDMFT), a strongly correlated system is represented by a small cluster of correlated sites, coupled to an adjustable bath of uncorrelated sites simulating the cluster's environment; the parameters governing the bath are set by a self-consistency condition involving the local Green function and the lattice electron dispersion. Solving the cluster problem with an exact diagonalization method is only practical for small bath sizes (8 sites). In that case the self-consistency condition cannot be exactly satisfied and is replaced by a minimization procedure. There is some freedom in the definition of the 'merit function' to optimize. We use Potthoff's Self-Energy Functional Approach on the one-and two-dimensional Hubbard models to gain insight into the best choice for this merit function. We argue that several merit functions should be used and preference given to the one that leads to the smallest gradient of the Potthoff self-energy functional. We propose a new merit function weighted with the self-energy that seems to fit the Mott transition in two dimensions better than other merit functions.
It is well known that cellular dynamical mean-field theory (CDMFT) leads to the artificial breaki... more It is well known that cellular dynamical mean-field theory (CDMFT) leads to the artificial breaking of translation invariance. In spite of this, it is one of the most successful methods to treat strongly correlated electrons systems. Here, we investigate in more detail how this broken translation invariance manifests itself. This allows to disentangle artificial broken translation invariance effects from the genuine strongly correlated effects captured by CDMFT. We report artificial density waves taking the shape of the cluster-cluster density wavesin all our zero temperature CDMFT solutions, including pair density waves in the superconducting state. We discuss the limitations of periodization regarding this phenomenon, and we present mean-field density-wave models that reproduce CDMFT results at low energy in the superconducting state. We then discuss how these artificial density waves help the agreement of CDMFT with high temperature superconducting cuprates regarding the low-energy spectrum, in particular for subgap structures observed in tunnelling microscopy. We relate these subgap structures to nodal and anti-nodal gaps in our results, similar to those observed in photoemission experiments. This fortuitous agreement suggests that spatial inhomogeneity may be a key ingredient to explain some features of the low-energy underdoped spectrum of cuprates with strongly correlated methods. This work deepens our understanding of CDMFT and clearly identifies signatures of broken translation invariance in the presence of strong correlations.
This is a short review of the theoretical work on the two-dimensional Hubbard model performed in ... more This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments has been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the Two-Particle Self-Consistent Approach, Variational Cluster Perturbation Theory (or variational cluster approximation), and Cellular Dynamical Mean-Field Theory.
Weyl semimetals, featuring massless linearly dispersing chiral fermions in three dimensions, prov... more Weyl semimetals, featuring massless linearly dispersing chiral fermions in three dimensions, provide an excellent platform for studying the interplay of electronic interactions and topology, and exploring new correlated states of matter. Here, we examine the effect of a local repulsive interaction on an inversionsymmetry breaking Weyl semimetal model, using cluster dynamical mean field theory and variational cluster approximation methods. Our analysis reveals a continuous transition from the gapless Weyl semimetal phase to a gapped spin density wave ordered phase at a critical value of the interaction, which is determined by the band structure parameters. Further, we introduce a finite tilt in the linear dispersion and examine the corresponding behavior for a type-II Weyl semimetal model, where the critical interaction strength is found to be significantly diminished, indicating a greater susceptibility towards interactions. The behavior of different physical quantities, such as the double occupancy, the spectral function and the Berry curvature associated with the Weyl nodes are obtained in both the semimetallic and the magnetically ordered states. Finally, we provide an interaction-induced phase diagram for the Weyl semimetal model, as a function of the tilt parameter.
We investigate the possibility of spin texture in the bilayer cuprate superconductor Bi 2 Sr 2 Ca... more We investigate the possibility of spin texture in the bilayer cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+δ using cluster dynamical mean field theory (CDMFT). The one-band Hubbard model with a small interlayer hopping and a Rashba spin-orbit coupling is used to describe the material. The d-wave order parameter is not much affected by the presence of the Rashba coupling, but a small triplet component appears. We find a spin texture circulating in the same direction around k = (0, 0) and k = (π, π) and stable against the superconducting phase. The amplitude of the spin structure, however, is strongly affected by the pseudogap phenomenon, more so than the spectral function itself. While electron-electron interactions are a key ingredient in the study of quantum materials, the presence of a spin-orbit coupling (SOC) is the source of new emergent phenomena, especially in heavy transition metal compounds . The SOC is a key ingredient of the topological states of matter [2, 3]. The interplay or competition between SOC and electron correlations is relevant in systems like the heavy fermion superlattices [4], iridium oxides [5], and optical lattices [6], in which exotic phases are expected. Within the Rashba-Hubbard model, a mixed singlet-triplet superconducting state [7-15], novel magnetism , and nontrivial topological properties are theoretically predicted.
We study the charge-density-wave order and its competition with superconductivity in the one-band... more We study the charge-density-wave order and its competition with superconductivity in the one-band Hubbard model for high-T c superconducting cuprates. We use cluster dynamical mean field theory (CDMFT) at T = 0. The one-band Hubbard model only contains copper atoms, and a physical charge-density-wave with charge excesses located on the oxygen atoms manifests itself as a bond-density-wave (BDW) within this context. It arises purely out of local correlation effects and also leads to a s -wave pair-density-wave in the presence of d-wave superconductivity. The d-wave BDW is suppressed on increasing U and is favored on increasing the magnitude of the second-neighbor hopping t . Further, the d-wave BDW order is weakened when in competition with superconductivity, as seen in experiments. Additionally it behaves quite differently on varying U in the superconducting state compared to the normal state.
The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at stro... more The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at strong coupling, interpolates between the Heisenberg model and the Kitaev model. It is basically a Hubbard model with ordinary hopping t and spin-dependent hopping t . We study this model in the weak to intermediate coupling regime, at half-filling, using the Cellular Dynamical Impurity Approximation (CDIA), an approach related to Dynamical Mean Field Theory but based on Potthoff's variational principle. We identify four phases in the (U, t ) plane: two semi-metallic phases with different numbers of Dirac points, an antiferromagnetic insulator, and an algebraic spin liquid. The last two are separated by a first-order transition. These four phases all meet at a single point and could be realized in cold atom systems.
We use a tensor network method to compute the low-energy excitations of a large-scale fluxonium q... more We use a tensor network method to compute the low-energy excitations of a large-scale fluxonium qubit up to a desired accuracy. We employ this numerical technique to estimate the pure-dephasing coherence time of the fluxonium qubit due to charge noise and coherent quantum phase slips from first principles, finding an agreement with previously obtained experimental results. By developing an accurate single-mode theory that captures the details of the fluxonium device, we benchmark the results obtained with the tensor network for circuits spanning a Hilbert space as large as 15 180 . Our algorithm is directly applicable to the wide variety of circuit-QED systems and may be a useful tool for scaling up superconducting quantum technologies.
We study the spinful fermionic Haldane-Hubbard model at half filling using a combination of quant... more We study the spinful fermionic Haldane-Hubbard model at half filling using a combination of quantum cluster methods: cluster perturbation theory (CPT), the variational cluster approximation (VCA), and cluster dynamical mean-field theory (CDMFT). We explore possible zero-temperature phases of the model as a function of on-site repulsive interaction strength and next-nearest-neighbor hopping amplitude and phase. Our approach allows us to access the regime of intermediate interaction strength, where charge fluctuations are significant and effective spin model descriptions may not be justified. Our approach also improves upon mean-field solutions of the Haldane-Hubbard model by retaining local quantum fluctuations and treating them nonperturbatively. We find a correlated topological Chern insulator for weak interactions and a topologically trivial Néel antiferromagnetic insulator for strong interactions. For intermediate interactions, we find that topologically nontrivial Néel antiferromagnetic insulating phases and/or a topologically nontrivial nonmagnetic insulating phase may be stabilized.
Superfluid stiffness ρs is a defining characteristic of the superconducting state, allowing phase... more Superfluid stiffness ρs is a defining characteristic of the superconducting state, allowing phase coherence and supercurrent. It is accessible experimentally through the penetration depth. Coexistence of d-wave superconductivity with other phases in underdoped cuprates, such as antiferromagnetism (AF) or charge-density waves (CDW), may drastically alter ρs. To shed light on this physics, the zero-temperature value of ρs = ρzz along the c-axis was computed for different values of Hubbard interaction U and different sets of tight-binding parameters describing the high-temperature superconductors YBCO and NCCO. We used Cellular Dynamical Mean-Field Theory for the one-band Hubbard model with exact diagonalization as impurity solver and state-of-the-art bath parametrization. We conclude that Mott physics plays a dominant role in determining the superfluid stiffness on the hole-doped side of the phase diagram. On the electron-doped side, antiferromagnetism wins over superconductivity near half-filling. But upon approaching optimal electron-doping, homogeneous coexistence between superconductivity and antiferromagnetism causes the superfluid stiffness to drop sharply. Hence, on the electron-doped side, it is competition between antiferromagnetism and d-wave superconductivity that plays a dominant role in determining the value of ρzz near half-filling. At large overdoping, ρzz behaves in a more BCS-like manner in both the electron-and hole-doped cases. We comment on some qualitative implications of these results for the superconducting transition temperature.
Superfluid stiffness ρs is a defining characteristic of the superconducting state, allowing phase... more Superfluid stiffness ρs is a defining characteristic of the superconducting state, allowing phase coherence and supercurrent. It is accessible experimentally through the penetration depth. Coexistence of d-wave superconductivity with other phases in underdoped cuprates, such as antiferromagnetism (AF) or charge-density waves (CDW), may drastically alter ρs. To shed light on this physics, the zero-temperature value of ρs = ρzz along the c-axis was computed for different values of Hubbard interaction U and different sets of tight-binding parameters describing the high-temperature superconductors YBCO and NCCO. We used Cellular Dynamical Mean-Field Theory for the one-band Hubbard model with exact diagonalization as impurity solver and state-of-the-art bath parametrization. We conclude that Mott physics plays a dominant role in determining the superfluid stiffness on the hole-doped side of the phase diagram. On the electron-doped side, antiferromagnetism wins over superconductivity near half-filling. But upon approaching optimal electron-doping, homogeneous coexistence between superconductivity and antiferromagnetism causes the superfluid stiffness to drop sharply. Hence, on the electron-doped side, it is competition between antiferromagnetism and d-wave superconductivity that plays a dominant role in determining the value of ρzz near half-filling. At large overdoping, ρzz behaves in a more BCS-like manner in both the electron-and hole-doped cases. We comment on some qualitative implications of these results for the superconducting transition temperature.
The presence of incommensurate spiral spin-density waves (SDW) has been proposed to explain the p... more The presence of incommensurate spiral spin-density waves (SDW) has been proposed to explain the p (hole doping) to 1 + p jump measured in the Hall number nH at a doping p * . Here we explore incommensurate collinear SDW as another possible explanation of this phenomenon, distinct from the incommensurate spiral SDW proposal. We examine the effect of different SDW strengths and wavevectors and we find that the nH ∼ p behavior is hardly reproduced at low doping. Furthermore, the calculated nH and Fermi surfaces give characteristic features that should be observed, thus the lack of these features in experiment suggests that the incommensurate collinear SDW is unlikely to be a good candidate to explain the nH ∼ p observed in the pseudogap regime.
International Journal of Modern Physics, Apr 1, 1992
We study the nonunitary diagonal cosets constructed from admissible representations of Kač-Moody ... more We study the nonunitary diagonal cosets constructed from admissible representations of Kač-Moody algebras at fractional level, with an emphasis on the question of field identification. Generic classes of field identifications are obtained from the analysis of the modular S matrix. These include the usual class related to outer automorphisms, as well as some intrinsically nonunitary field identifications. They allow for a simple choice of coset field representatives where all field components of the coset are associated with integrable finite weights.
It has been argued that inhomogeneity generally can enhance superconductivity in the cuprate high... more It has been argued that inhomogeneity generally can enhance superconductivity in the cuprate high-Tc materials. To check the validity of this claim, we study d-wave superconductivity on the checkerboard Hubbard model on a square lattice using the Cellular Dynamical Mean Field theory method with an exact diagonalization solver at zero temperature. The d-wave order parameter is computed for various inhomogeneity levels over the entire doping range of interest in both strong and weak coupling regimes. At a given doping, the size of the d-wave order parameter manifests itself directly in the height of the coherence peaks and hence is an appropriate measure of the strength of superconductivity. The weak coupling results reveal a suppression of the order parameter in the presence of inhomogeneity for small to intermediate hole dopings, while it is enhanced for large dopings. In contrast, for strong coupling there is a monotonic decrease in the maximum amplitude of the superconducting order parameter with inhomogeneity over the entire doping range of interest. Furthermore, at moderately high inhomogeneity, the system undergoes a first-order transition from the superconducting to the normal state in the underdoped regime. In the overdoped regime, the change in the value of the superconducting order parameter correlates with the height of the lowest energy peak in the spectral weight of antiferromagnetic spin fluctuations, confirming the connection between antiferromagnetic fluctuations and d-wave superconductivity found in earlier studies on the homogeneous case. Our results are benchmarked by comparisons with numerically exact results on the checkerboard Hubbard ladder. I.
This is an expanded version of a lecture given at the Workshop on Theoretical Methods for Strongl... more This is an expanded version of a lecture given at the Workshop on Theoretical Methods for Strongly Correlated Fermions, held at the Centre de Recherches Mathématiques, in Montréal, from May 26 to May 30, 1999. After general comments on the relevance of field theory to condensed matter systems, the continuum description of interacting electrons in 1D is summarized. The bosonization procedure is then introduced heuristically, but the precise quantum equivalence between fermion and boson is also presented. Then the exact solution of the Tomonaga-Luttinger model is carried out. Two other applications of bosonization are then sketched. We end with a quick introduction to non-Abelian bosonization.
We apply the finite-temperature renormalization-group (RG) to a model based on an effective actio... more We apply the finite-temperature renormalization-group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation invariant Fermi surface. The basic quantities of Fermi liquid theory, the Landau function and the scattering vertex, are calculated as fixed points of the RG flow in terms of the effective action's interaction function. The classic derivations of Fermi liquid theory, which apply the Bethe-Salpeter equation and amount to summing direct particle-hole ladder diagrams, neglect the zeroangle singularity in the exchange particle-hole loop. As a consequence, the antisymmetry of the forward scattering vertex is not guaranteed and the amplitude sum rule must be imposed by hand on the components of the Landau function. We show that the strong interference of the direct and exchange processes of particle-hole scattering near zero angle invalidates the ladder approximation in this region, resulting in temperature-dependent narrow-angle anomalies in the Landau function and scattering vertex. In this RG approach the Pauli principle is automatically satisfied. The consequences of the RG corrections on Fermi liquid theory are discussed. In particular, we show that the amplitude sum rule is not valid.
The antiferromagnetic Heisenberg model on a chain with nearest and next nearest neighbor coupling... more The antiferromagnetic Heisenberg model on a chain with nearest and next nearest neighbor couplings is mapped onto the SO(3) nonlinear sigma model in the continuum limit. In one spatial dimension this model is always in its disordered phase and a gap opens to excited states. The latter form a doubly degenerate spin-1 branch at all orders in 1/N . We argue that this feature should be present in the spin-1 Heisenberg model itself. Exact diagonalizations are used to support this claim. The inapplicability of this model to half-integer spin chains is discussed.
We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle θ = 53.13 • using ... more We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle θ = 53.13 • using the variational cluster approximation, a method that treats short-range dynamical correlations exactly. At intermediate interlayer tunneling, the phase difference φ between the d-wave order parameters of two layers is π in the overdoped regime, while it is zero in the underdoped regime, close to the Mott phase. At strong interlayer tunneling, we observe a clear time-reversal symmetry breaking phase near optimal doping, in which the phase difference φ changes continuously from 0 to π. However, this phase has trivial topology. We also apply a cluster extension of dynamical mean field theory to the same problem, but fail to detect a time-reversal breaking phase with that method.
We study the one-band Hubbard model on the trellis lattice, a two-dimensional frustrated lattice ... more We study the one-band Hubbard model on the trellis lattice, a two-dimensional frustrated lattice of coupled two-leg ladders, with hopping amplitude t within ladders and t between ladders. For large U/t this is a model for the cuprate Sr14-xCaxCu24O41. We investigate the phase diagram as a function of doping for U = 10t using two quantum cluster methods: The variational cluster approximation (VCA), with clusters of sizes 8 and 12, and Cellular dynamical mean field theory (CDMFT), both at zero temperature. Both methods predict a superconducting dome, ending at roughly 20% doping in VCA and 15% in CDMFT. In VCA, the superconducting order parameter is complex in a range of doping centered around 10%, corresponding to bulk chiral, T -violating superconductivity. However, the CDMFT solution is not chiral. We find evidence for a migration of the Cooper pairs from the inter-ladder region towards the plaquettes as doping is increased.
The onset of the pseudogap in high-T c superconducting cuprates (HTSC) is marked by the T * line ... more The onset of the pseudogap in high-T c superconducting cuprates (HTSC) is marked by the T * line in the doping-temperature phase diagram, which ends at a point p * at zero temperature within the superconducting dome. Although various theoretical and experimental studies indicate a competition between the pseudogap and superconductivity, there is no general consensus on the effects of the pseudogap within the superconducting phase. We use cluster dynamical mean field theory on a three-band Hubbard model for the HTSC to study the superconducting phase at T = 0, obtained when doping the charge-transfer insulator, for several values of U. We observe a first-order transition within the superconducting phase, which separates the underdoped and overdoped solutions. The transition to the underdoped solution is marked by a discontinuous increase in the spectral gap, and on further underdoping the spectral gap increases while the superconducting order parameter decreases. We conclude that this is due to the onset of the pseudogap in the underdoped region, which contributes to the increasing spectral gap; this is further consistent with the appearance of a pole in the normal component of the self-energy, in the antinodal region, in the underdoped solution. This is accompanied by a change in the source of the condensation energy from potential energy, in the overdoped region, to kinetic energy in the underdoped region. Further, we also observe that the d-wave node vanishes smoothly within the superconducting phase at low values of hole doping, within the underdoped region. We see this as a manifestation of Mott physics operating at very low doping. Various aspects of the results and their implications are discussed.
In the Cellular Dynamical Mean Field Theory (CDMFT), a strongly correlated system is represented ... more In the Cellular Dynamical Mean Field Theory (CDMFT), a strongly correlated system is represented by a small cluster of correlated sites, coupled to an adjustable bath of uncorrelated sites simulating the cluster's environment; the parameters governing the bath are set by a self-consistency condition involving the local Green function and the lattice electron dispersion. Solving the cluster problem with an exact diagonalization method is only practical for small bath sizes (8 sites). In that case the self-consistency condition cannot be exactly satisfied and is replaced by a minimization procedure. There is some freedom in the definition of the 'merit function' to optimize. We use Potthoff's Self-Energy Functional Approach on the one-and two-dimensional Hubbard models to gain insight into the best choice for this merit function. We argue that several merit functions should be used and preference given to the one that leads to the smallest gradient of the Potthoff self-energy functional. We propose a new merit function weighted with the self-energy that seems to fit the Mott transition in two dimensions better than other merit functions.
It is well known that cellular dynamical mean-field theory (CDMFT) leads to the artificial breaki... more It is well known that cellular dynamical mean-field theory (CDMFT) leads to the artificial breaking of translation invariance. In spite of this, it is one of the most successful methods to treat strongly correlated electrons systems. Here, we investigate in more detail how this broken translation invariance manifests itself. This allows to disentangle artificial broken translation invariance effects from the genuine strongly correlated effects captured by CDMFT. We report artificial density waves taking the shape of the cluster-cluster density wavesin all our zero temperature CDMFT solutions, including pair density waves in the superconducting state. We discuss the limitations of periodization regarding this phenomenon, and we present mean-field density-wave models that reproduce CDMFT results at low energy in the superconducting state. We then discuss how these artificial density waves help the agreement of CDMFT with high temperature superconducting cuprates regarding the low-energy spectrum, in particular for subgap structures observed in tunnelling microscopy. We relate these subgap structures to nodal and anti-nodal gaps in our results, similar to those observed in photoemission experiments. This fortuitous agreement suggests that spatial inhomogeneity may be a key ingredient to explain some features of the low-energy underdoped spectrum of cuprates with strongly correlated methods. This work deepens our understanding of CDMFT and clearly identifies signatures of broken translation invariance in the presence of strong correlations.
This is a short review of the theoretical work on the two-dimensional Hubbard model performed in ... more This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments has been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the Two-Particle Self-Consistent Approach, Variational Cluster Perturbation Theory (or variational cluster approximation), and Cellular Dynamical Mean-Field Theory.
Weyl semimetals, featuring massless linearly dispersing chiral fermions in three dimensions, prov... more Weyl semimetals, featuring massless linearly dispersing chiral fermions in three dimensions, provide an excellent platform for studying the interplay of electronic interactions and topology, and exploring new correlated states of matter. Here, we examine the effect of a local repulsive interaction on an inversionsymmetry breaking Weyl semimetal model, using cluster dynamical mean field theory and variational cluster approximation methods. Our analysis reveals a continuous transition from the gapless Weyl semimetal phase to a gapped spin density wave ordered phase at a critical value of the interaction, which is determined by the band structure parameters. Further, we introduce a finite tilt in the linear dispersion and examine the corresponding behavior for a type-II Weyl semimetal model, where the critical interaction strength is found to be significantly diminished, indicating a greater susceptibility towards interactions. The behavior of different physical quantities, such as the double occupancy, the spectral function and the Berry curvature associated with the Weyl nodes are obtained in both the semimetallic and the magnetically ordered states. Finally, we provide an interaction-induced phase diagram for the Weyl semimetal model, as a function of the tilt parameter.
We investigate the possibility of spin texture in the bilayer cuprate superconductor Bi 2 Sr 2 Ca... more We investigate the possibility of spin texture in the bilayer cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+δ using cluster dynamical mean field theory (CDMFT). The one-band Hubbard model with a small interlayer hopping and a Rashba spin-orbit coupling is used to describe the material. The d-wave order parameter is not much affected by the presence of the Rashba coupling, but a small triplet component appears. We find a spin texture circulating in the same direction around k = (0, 0) and k = (π, π) and stable against the superconducting phase. The amplitude of the spin structure, however, is strongly affected by the pseudogap phenomenon, more so than the spectral function itself. While electron-electron interactions are a key ingredient in the study of quantum materials, the presence of a spin-orbit coupling (SOC) is the source of new emergent phenomena, especially in heavy transition metal compounds . The SOC is a key ingredient of the topological states of matter [2, 3]. The interplay or competition between SOC and electron correlations is relevant in systems like the heavy fermion superlattices [4], iridium oxides [5], and optical lattices [6], in which exotic phases are expected. Within the Rashba-Hubbard model, a mixed singlet-triplet superconducting state [7-15], novel magnetism , and nontrivial topological properties are theoretically predicted.
We study the charge-density-wave order and its competition with superconductivity in the one-band... more We study the charge-density-wave order and its competition with superconductivity in the one-band Hubbard model for high-T c superconducting cuprates. We use cluster dynamical mean field theory (CDMFT) at T = 0. The one-band Hubbard model only contains copper atoms, and a physical charge-density-wave with charge excesses located on the oxygen atoms manifests itself as a bond-density-wave (BDW) within this context. It arises purely out of local correlation effects and also leads to a s -wave pair-density-wave in the presence of d-wave superconductivity. The d-wave BDW is suppressed on increasing U and is favored on increasing the magnitude of the second-neighbor hopping t . Further, the d-wave BDW order is weakened when in competition with superconductivity, as seen in experiments. Additionally it behaves quite differently on varying U in the superconducting state compared to the normal state.
The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at stro... more The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at strong coupling, interpolates between the Heisenberg model and the Kitaev model. It is basically a Hubbard model with ordinary hopping t and spin-dependent hopping t . We study this model in the weak to intermediate coupling regime, at half-filling, using the Cellular Dynamical Impurity Approximation (CDIA), an approach related to Dynamical Mean Field Theory but based on Potthoff's variational principle. We identify four phases in the (U, t ) plane: two semi-metallic phases with different numbers of Dirac points, an antiferromagnetic insulator, and an algebraic spin liquid. The last two are separated by a first-order transition. These four phases all meet at a single point and could be realized in cold atom systems.
We use a tensor network method to compute the low-energy excitations of a large-scale fluxonium q... more We use a tensor network method to compute the low-energy excitations of a large-scale fluxonium qubit up to a desired accuracy. We employ this numerical technique to estimate the pure-dephasing coherence time of the fluxonium qubit due to charge noise and coherent quantum phase slips from first principles, finding an agreement with previously obtained experimental results. By developing an accurate single-mode theory that captures the details of the fluxonium device, we benchmark the results obtained with the tensor network for circuits spanning a Hilbert space as large as 15 180 . Our algorithm is directly applicable to the wide variety of circuit-QED systems and may be a useful tool for scaling up superconducting quantum technologies.
We study the spinful fermionic Haldane-Hubbard model at half filling using a combination of quant... more We study the spinful fermionic Haldane-Hubbard model at half filling using a combination of quantum cluster methods: cluster perturbation theory (CPT), the variational cluster approximation (VCA), and cluster dynamical mean-field theory (CDMFT). We explore possible zero-temperature phases of the model as a function of on-site repulsive interaction strength and next-nearest-neighbor hopping amplitude and phase. Our approach allows us to access the regime of intermediate interaction strength, where charge fluctuations are significant and effective spin model descriptions may not be justified. Our approach also improves upon mean-field solutions of the Haldane-Hubbard model by retaining local quantum fluctuations and treating them nonperturbatively. We find a correlated topological Chern insulator for weak interactions and a topologically trivial Néel antiferromagnetic insulator for strong interactions. For intermediate interactions, we find that topologically nontrivial Néel antiferromagnetic insulating phases and/or a topologically nontrivial nonmagnetic insulating phase may be stabilized.
Superfluid stiffness ρs is a defining characteristic of the superconducting state, allowing phase... more Superfluid stiffness ρs is a defining characteristic of the superconducting state, allowing phase coherence and supercurrent. It is accessible experimentally through the penetration depth. Coexistence of d-wave superconductivity with other phases in underdoped cuprates, such as antiferromagnetism (AF) or charge-density waves (CDW), may drastically alter ρs. To shed light on this physics, the zero-temperature value of ρs = ρzz along the c-axis was computed for different values of Hubbard interaction U and different sets of tight-binding parameters describing the high-temperature superconductors YBCO and NCCO. We used Cellular Dynamical Mean-Field Theory for the one-band Hubbard model with exact diagonalization as impurity solver and state-of-the-art bath parametrization. We conclude that Mott physics plays a dominant role in determining the superfluid stiffness on the hole-doped side of the phase diagram. On the electron-doped side, antiferromagnetism wins over superconductivity near half-filling. But upon approaching optimal electron-doping, homogeneous coexistence between superconductivity and antiferromagnetism causes the superfluid stiffness to drop sharply. Hence, on the electron-doped side, it is competition between antiferromagnetism and d-wave superconductivity that plays a dominant role in determining the value of ρzz near half-filling. At large overdoping, ρzz behaves in a more BCS-like manner in both the electron-and hole-doped cases. We comment on some qualitative implications of these results for the superconducting transition temperature.
Superfluid stiffness ρs is a defining characteristic of the superconducting state, allowing phase... more Superfluid stiffness ρs is a defining characteristic of the superconducting state, allowing phase coherence and supercurrent. It is accessible experimentally through the penetration depth. Coexistence of d-wave superconductivity with other phases in underdoped cuprates, such as antiferromagnetism (AF) or charge-density waves (CDW), may drastically alter ρs. To shed light on this physics, the zero-temperature value of ρs = ρzz along the c-axis was computed for different values of Hubbard interaction U and different sets of tight-binding parameters describing the high-temperature superconductors YBCO and NCCO. We used Cellular Dynamical Mean-Field Theory for the one-band Hubbard model with exact diagonalization as impurity solver and state-of-the-art bath parametrization. We conclude that Mott physics plays a dominant role in determining the superfluid stiffness on the hole-doped side of the phase diagram. On the electron-doped side, antiferromagnetism wins over superconductivity near half-filling. But upon approaching optimal electron-doping, homogeneous coexistence between superconductivity and antiferromagnetism causes the superfluid stiffness to drop sharply. Hence, on the electron-doped side, it is competition between antiferromagnetism and d-wave superconductivity that plays a dominant role in determining the value of ρzz near half-filling. At large overdoping, ρzz behaves in a more BCS-like manner in both the electron-and hole-doped cases. We comment on some qualitative implications of these results for the superconducting transition temperature.
The presence of incommensurate spiral spin-density waves (SDW) has been proposed to explain the p... more The presence of incommensurate spiral spin-density waves (SDW) has been proposed to explain the p (hole doping) to 1 + p jump measured in the Hall number nH at a doping p * . Here we explore incommensurate collinear SDW as another possible explanation of this phenomenon, distinct from the incommensurate spiral SDW proposal. We examine the effect of different SDW strengths and wavevectors and we find that the nH ∼ p behavior is hardly reproduced at low doping. Furthermore, the calculated nH and Fermi surfaces give characteristic features that should be observed, thus the lack of these features in experiment suggests that the incommensurate collinear SDW is unlikely to be a good candidate to explain the nH ∼ p observed in the pseudogap regime.
International Journal of Modern Physics, Apr 1, 1992
We study the nonunitary diagonal cosets constructed from admissible representations of Kač-Moody ... more We study the nonunitary diagonal cosets constructed from admissible representations of Kač-Moody algebras at fractional level, with an emphasis on the question of field identification. Generic classes of field identifications are obtained from the analysis of the modular S matrix. These include the usual class related to outer automorphisms, as well as some intrinsically nonunitary field identifications. They allow for a simple choice of coset field representatives where all field components of the coset are associated with integrable finite weights.
It has been argued that inhomogeneity generally can enhance superconductivity in the cuprate high... more It has been argued that inhomogeneity generally can enhance superconductivity in the cuprate high-Tc materials. To check the validity of this claim, we study d-wave superconductivity on the checkerboard Hubbard model on a square lattice using the Cellular Dynamical Mean Field theory method with an exact diagonalization solver at zero temperature. The d-wave order parameter is computed for various inhomogeneity levels over the entire doping range of interest in both strong and weak coupling regimes. At a given doping, the size of the d-wave order parameter manifests itself directly in the height of the coherence peaks and hence is an appropriate measure of the strength of superconductivity. The weak coupling results reveal a suppression of the order parameter in the presence of inhomogeneity for small to intermediate hole dopings, while it is enhanced for large dopings. In contrast, for strong coupling there is a monotonic decrease in the maximum amplitude of the superconducting order parameter with inhomogeneity over the entire doping range of interest. Furthermore, at moderately high inhomogeneity, the system undergoes a first-order transition from the superconducting to the normal state in the underdoped regime. In the overdoped regime, the change in the value of the superconducting order parameter correlates with the height of the lowest energy peak in the spectral weight of antiferromagnetic spin fluctuations, confirming the connection between antiferromagnetic fluctuations and d-wave superconductivity found in earlier studies on the homogeneous case. Our results are benchmarked by comparisons with numerically exact results on the checkerboard Hubbard ladder. I.
This is an expanded version of a lecture given at the Workshop on Theoretical Methods for Strongl... more This is an expanded version of a lecture given at the Workshop on Theoretical Methods for Strongly Correlated Fermions, held at the Centre de Recherches Mathématiques, in Montréal, from May 26 to May 30, 1999. After general comments on the relevance of field theory to condensed matter systems, the continuum description of interacting electrons in 1D is summarized. The bosonization procedure is then introduced heuristically, but the precise quantum equivalence between fermion and boson is also presented. Then the exact solution of the Tomonaga-Luttinger model is carried out. Two other applications of bosonization are then sketched. We end with a quick introduction to non-Abelian bosonization.
We apply the finite-temperature renormalization-group (RG) to a model based on an effective actio... more We apply the finite-temperature renormalization-group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation invariant Fermi surface. The basic quantities of Fermi liquid theory, the Landau function and the scattering vertex, are calculated as fixed points of the RG flow in terms of the effective action's interaction function. The classic derivations of Fermi liquid theory, which apply the Bethe-Salpeter equation and amount to summing direct particle-hole ladder diagrams, neglect the zeroangle singularity in the exchange particle-hole loop. As a consequence, the antisymmetry of the forward scattering vertex is not guaranteed and the amplitude sum rule must be imposed by hand on the components of the Landau function. We show that the strong interference of the direct and exchange processes of particle-hole scattering near zero angle invalidates the ladder approximation in this region, resulting in temperature-dependent narrow-angle anomalies in the Landau function and scattering vertex. In this RG approach the Pauli principle is automatically satisfied. The consequences of the RG corrections on Fermi liquid theory are discussed. In particular, we show that the amplitude sum rule is not valid.
The antiferromagnetic Heisenberg model on a chain with nearest and next nearest neighbor coupling... more The antiferromagnetic Heisenberg model on a chain with nearest and next nearest neighbor couplings is mapped onto the SO(3) nonlinear sigma model in the continuum limit. In one spatial dimension this model is always in its disordered phase and a gap opens to excited states. The latter form a doubly degenerate spin-1 branch at all orders in 1/N . We argue that this feature should be present in the spin-1 Heisenberg model itself. Exact diagonalizations are used to support this claim. The inapplicability of this model to half-integer spin chains is discussed.
We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle θ = 53.13 • using ... more We study the twisted Hubbard model of a cuprate bilayer at a fixed twist angle θ = 53.13 • using the variational cluster approximation, a method that treats short-range dynamical correlations exactly. At intermediate interlayer tunneling, the phase difference φ between the d-wave order parameters of two layers is π in the overdoped regime, while it is zero in the underdoped regime, close to the Mott phase. At strong interlayer tunneling, we observe a clear time-reversal symmetry breaking phase near optimal doping, in which the phase difference φ changes continuously from 0 to π. However, this phase has trivial topology. We also apply a cluster extension of dynamical mean field theory to the same problem, but fail to detect a time-reversal breaking phase with that method.
Cours de 3ème année du baccalauréat en physique de l'Université de Sherbrooke, une introduction à... more Cours de 3ème année du baccalauréat en physique de l'Université de Sherbrooke, une introduction à la physique théorique des particules élémentaires et au modèle standard.
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Papers by David Sénéchal