Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subject to har... more Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subject to harmonic trapping exhibit intriguing compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a random potential on these ground-state phases. Within a density-functional scheme we show that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the compressibility at low density from quenching of percolation.
For decades, the topological phenomena in quantum systems have always been catching our attention... more For decades, the topological phenomena in quantum systems have always been catching our attention. Recently, there are many interests on the systems where topologically protected edge states exist, even in the presence of non-Hermiticity. Motivated by these researches, the topological properties of a non-Hermitian dice model are studied in two non-Hermitian cases, viz. in the imbalanced and the balanced dissipations. Our results suggest that the topological phases are protected by the real gaps and the bulk-edge correspondence readily seen in the real edge-state spectra. Besides, we show that the principle of the bulk-edge correspondence in Hermitian case is still effective in analyzing the three-band non-Hermitian system. We find that there are topological non-trivial phases with large Chern numbers $C=-3$ robust against the dissipative perturbations.
arXiv: Disordered Systems and Neural Networks, 2020
We study a one-dimensional $p$-wave superconductor subject to non-Hermitian quasiperiodic potenti... more We study a one-dimensional $p$-wave superconductor subject to non-Hermitian quasiperiodic potentials. Although the existence of the non-Hermiticity, the Majorana zero mode is still robust against the disorder perturbation. The analytic topological phase boundary is verified by calculating the energy gap closing point and the topological invariant. Furthermore, we investigate the localized properties of this model, revealing that the topological phase transition is accompanied with the Anderson localization phase transition, and a wide critical phase emerges with amplitude increments of the non-Hermitian quasiperiodic potentials. Finally, we numerically uncover a non-conventional real-complex transition of the energy spectrum, which is different from the conventional $\mathcal{PT}$ symmetric transition.
The phase diagram of the one-dimensional attractive Fermi-Hubbard model trapped in a harmonic pot... more The phase diagram of the one-dimensional attractive Fermi-Hubbard model trapped in a harmonic potential was studied within the Tomas-Fermi approximation,which was based on the exactly solved Bethe-ansatz coupled equations.The compressibility,double occupancy,and its derivatives were calculated to measure the phase transition and the external potential induced by the system parameters.
arXiv: Disordered Systems and Neural Networks, 2020
Whether the many-body mobility edges can exist in a one-dimensional interacting quantum system is... more Whether the many-body mobility edges can exist in a one-dimensional interacting quantum system is a controversial problem, mainly hampered by the limited system sizes amenable to numerical simulations. We investigate the transition from chaos to localization by constructing a combined random matrix, which has two extremes, one of Gaussian orthogonal ensemble and the other of Poisson statistics, drawn from different distributions. We find that by fixing a scaling parameter, the mobility edges can exist while increasing the matrix dimension $D\rightarrow\infty$, depending on the distribution of matrix elements of the diagonal uncorrelated matrix. By applying those results to a specific one-dimensional isolated quantum system of random diagonal elements, we confirm the existence of a many-body mobility edge, connecting it with results on the onset of level repulsion extracted from ensembles of mixed random matrices.
In this paper, we numerically solve the thermodynamic Bethe-ansatz coupled equations for a one-di... more In this paper, we numerically solve the thermodynamic Bethe-ansatz coupled equations for a one-dimensional Hubbard model at finite temperature and obtain the second order thermodynamics properties, such as the specific heat, compressibility, and susceptibility. We find that these three quantities could embody the phase transitions of the system, from the vacuum state to the metallic state, from the metallic state to the Mott-insulating phase, from the Mott-insulating phase to the metallic state, and from the metallic state to the band-insulating phase. With the increase of temperature, the thermal fluctuation overwhelms the quantum fluctuations and the phase transition points disappear due to the destruction of the Mott-insulating phase. But in the case of the strong interaction strength, the Mott-insulating phase is robust, embodying the compressibility. Furthermore, we study the thermodynamic properties of the inhomogeneous Hubbard model with trapping potential. Making use of the ...
After a quench of transverse field, the asymptotic long-time state of Ising model displays a tran... more After a quench of transverse field, the asymptotic long-time state of Ising model displays a transition from a ferromagnetic phase to a paramagnetic phase as the post-quench field strength increases, which is revealed by the vanishing of the order parameter defined as the averaged magnetization over time. We estimate the critical behavior of the magnetization at this nonequilibrium phase transition by using mean-field approximation. In the vicinity of the critical field, the magnetization vanishes as the inverse of a logarithmic function, which is significantly distinguished from the critical behavior of order parameter at the corresponding equilibrium phase transition, i.e. a power-law function.
In the framework of the tight binding approximation, we study a non-interacting model on the thre... more In the framework of the tight binding approximation, we study a non-interacting model on the three-component dice lattice with real nearest-neighbor and complex next-nearest-neighbor hopping subjected to $\Lambda$- or V-type sublattice potentials. By analyzing the dispersions of corresponding energy bands, we find that the system undergoes a metal-insulator transition which can be modulated not only by the Fermi energy but also the tunable extra parameters. Furthermore, rich topological phases, including the ones with high Hall plateau, are uncovered by calculating the associated band's Chern number. Besides, we also analyze the edge-state spectra and discuss the correspondence between Chern numbers and the edge states by the principle of bulk-edge correspondence.
arXiv: Disordered Systems and Neural Networks, 2016
We study a one-dimensional quasiperiodic system described by the off-diagonal Aubry-Andr\'{e}... more We study a one-dimensional quasiperiodic system described by the off-diagonal Aubry-Andr\'{e} model and investigate its phase diagram by using the symmetry and the multifractal analysis. It was shown in a recent work ({\it Phys. Rev. B} {\bf 93}, 205441 (2016)) that its phase diagram was divided into three regions, dubbed the extended, the topologically-nontrivial localized and the topologically-trivial localized phases, respectively. Out of our expectation, we find an additional region of the extended phase which can be mapped into the original one by a symmetry transformation. More unexpectedly, in both "localized" phases, most of the eigenfunctions are neither localized nor extended. Instead, they display critical features, that is, the minimum of the singularity spectrum is in a range $0<\gamma_{min}<1$ instead of $0$ for the localized state or $1$ for the extended state. Thus, a mixed phase is found with a mixture of localized and critical eigenfunctions.
Casimir effects manifests that, the two closely paralleled plates, generally produce a macroscopi... more Casimir effects manifests that, the two closely paralleled plates, generally produce a macroscopic attractive force due to the quantum vacuum fluctuations of the electromagnetic fields. The derivation of the force requires an {\it artificial} regulator by removing the divergent summation. By including naturally a spectrum density factor, based on the observation that an incomplete eigenvectors of observable, such as the eigenstates for the photons in the free field, can form a complete set of eigenvectors by introducing a unique spectrum transformation, an alternative way is presented to rederive the force, without using a regulator. As a result, the Casimir forces are obtained with the first term $-\pi^2 \hbar c/(240 a^4)$ attractive, and the second one, $-\pi^4 \hbar c^3 \sigma^2/(1008 a^6)$, also attractive but smaller, with $a$ the plate separation, and $\sigma$ a to-be-determined small constant number in the spectrum density factor.
We investigate the quench dynamics of a one-dimensional incommensurate lattice described by the A... more We investigate the quench dynamics of a one-dimensional incommensurate lattice described by the Aubry-André model by a sudden change of the strength of incommensurate potential ∆ and unveil that the dynamical signature of localization-delocalization transition can be characterized by the occurrence of zero points in the Loschmit echo. For the quench process with quenching taking place between two limits of ∆ = 0 and ∆ = ∞, we give analytical expressions of the Loschmidt echo, which indicate the existence of a series of zero points in the Loschmidt echo. For a general quench process, we calculate the Loschmidt echo numerically and analyze its statistical behavior. Our results show that if both the initial and post-quench Hamiltonian are in extended phase or localized phase, Loschmidt echo will always be greater than a positive number; however if they locate in different phases, Loschmidt echo can reach nearby zero at some time intervals.
We investigate the nonequilibrium dynamics of the one-dimension Aubry-André-Harper model with p-w... more We investigate the nonequilibrium dynamics of the one-dimension Aubry-André-Harper model with p-wave superconductivity by changing the potential strength with slow and sudden quench. Firstly, we study the slow quench dynamics from the localized phase to the critical phase by linearly decreasing the potential strength V. The localization length is finite and its scaling obeys the Kibble-Zurek mechanism. The results show that the second-order phase transition line shares the same critical exponent zν, giving the correlation length ν = 1 and dynamical exponent z = 1.373 ± 0.023, which are different from the Aubry-André model. Secondly, we also study the sudden quench dynamics between three different phases: localized phase, critical phase, and extended phase. In the limit of V = 0 and V = ∞, we analytically study the sudden quench dynamics via the Loschmidt echo. The results suggest that, if the initial state and the post-quench Hamiltonian are in different phases, the Loschmidt echo vanishes at some time intervals. Furthermore, we found that, if the initial value is in the critical phase, the direction of quenching is the same as one of the two limits mentioned before, and similar behaviors will occur.
With respect to the quantum anomalous Hall effect (QAHE), the detection of topological nontrivial... more With respect to the quantum anomalous Hall effect (QAHE), the detection of topological nontrivial large-Chern-number phases is an intriguing subject. Motivated by recent research on Floquet topological phases, this study proposes a periodic driving protocol to engineer large-Chern-number phases using the QAHE. Herein, spinless ultracold fermionic atoms are studied in a two-dimensional optical dice lattice with nearest-neighbor hopping and a-or V-type sublattice potential subjected to a circular driving force. Results suggest that large-Chern-number phases exist with Chern numbers C = −3, which is consistent with the edge-state quasienergy spectra.
The existence of many-body mobility edges in closed quantum systems has been the focus of intense... more The existence of many-body mobility edges in closed quantum systems has been the focus of intense debate after the emergence of the description of the many-body localization phenomenon. Here we propose that this issue can be settled in experiments by investigating the time evolution of local degrees of freedom, tailored for specific energies and intial states. An interacting model of spinless fermions with exponentially long-ranged tunneling amplitudes, whose non-interacting version known to display single-particle mobility edges, is used as the starting point upon which nearest-neighbor interactions are included. We verify the manifestation of many-body mobility edges by using numerous probes, suggesting that one cannot explain their appearance as merely being a result of finite-size effects.
We study a one-dimensional quasiperiodic system described by the Aubry-André model in the small w... more We study a one-dimensional quasiperiodic system described by the Aubry-André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry-André model are either extended or localized depending on the strength of incommensurate potential V being less or bigger than a critical value Vc, and thus no mobility edge exists. However, it was shown in a recent work that this conclusion does not hold true when the wave vector α of the incommensurate potential is small, and for the system with V < Vc, there exist almost mobility edges at the energy Ec ± , which separate the robustly delocalized states from "almost localized" states. We find that, besides Ec ± , there exist additionally another energy edges E c ′ ± , at which abrupt change of inverse participation ratio occurs. By using the inverse participation ratio and carrying out multifractal analyses, we identify the existence of critical regions among |Ec ± | ≤ |E| ≤ |E c ′ ± | with the almost mobility edges Ec ± and E c ′ ± separating the critical region from the extended and localized regions, respectively. We also study the system with V > Vc, for which all eigenstates are localized states, but can be divided into extended, critical and localized states in their dual space by utilizing the self-duality property of the Aubry-André model.
Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subject to har... more Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subject to harmonic trapping exhibit intriguing compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a random potential on these ground-state phases. Within a density-functional scheme we show that disorder has two main effects: (i) it destroys the local insulating regions if it is sufficiently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the compressibility at low density from quenching of percolation.
For decades, the topological phenomena in quantum systems have always been catching our attention... more For decades, the topological phenomena in quantum systems have always been catching our attention. Recently, there are many interests on the systems where topologically protected edge states exist, even in the presence of non-Hermiticity. Motivated by these researches, the topological properties of a non-Hermitian dice model are studied in two non-Hermitian cases, viz. in the imbalanced and the balanced dissipations. Our results suggest that the topological phases are protected by the real gaps and the bulk-edge correspondence readily seen in the real edge-state spectra. Besides, we show that the principle of the bulk-edge correspondence in Hermitian case is still effective in analyzing the three-band non-Hermitian system. We find that there are topological non-trivial phases with large Chern numbers $C=-3$ robust against the dissipative perturbations.
arXiv: Disordered Systems and Neural Networks, 2020
We study a one-dimensional $p$-wave superconductor subject to non-Hermitian quasiperiodic potenti... more We study a one-dimensional $p$-wave superconductor subject to non-Hermitian quasiperiodic potentials. Although the existence of the non-Hermiticity, the Majorana zero mode is still robust against the disorder perturbation. The analytic topological phase boundary is verified by calculating the energy gap closing point and the topological invariant. Furthermore, we investigate the localized properties of this model, revealing that the topological phase transition is accompanied with the Anderson localization phase transition, and a wide critical phase emerges with amplitude increments of the non-Hermitian quasiperiodic potentials. Finally, we numerically uncover a non-conventional real-complex transition of the energy spectrum, which is different from the conventional $\mathcal{PT}$ symmetric transition.
The phase diagram of the one-dimensional attractive Fermi-Hubbard model trapped in a harmonic pot... more The phase diagram of the one-dimensional attractive Fermi-Hubbard model trapped in a harmonic potential was studied within the Tomas-Fermi approximation,which was based on the exactly solved Bethe-ansatz coupled equations.The compressibility,double occupancy,and its derivatives were calculated to measure the phase transition and the external potential induced by the system parameters.
arXiv: Disordered Systems and Neural Networks, 2020
Whether the many-body mobility edges can exist in a one-dimensional interacting quantum system is... more Whether the many-body mobility edges can exist in a one-dimensional interacting quantum system is a controversial problem, mainly hampered by the limited system sizes amenable to numerical simulations. We investigate the transition from chaos to localization by constructing a combined random matrix, which has two extremes, one of Gaussian orthogonal ensemble and the other of Poisson statistics, drawn from different distributions. We find that by fixing a scaling parameter, the mobility edges can exist while increasing the matrix dimension $D\rightarrow\infty$, depending on the distribution of matrix elements of the diagonal uncorrelated matrix. By applying those results to a specific one-dimensional isolated quantum system of random diagonal elements, we confirm the existence of a many-body mobility edge, connecting it with results on the onset of level repulsion extracted from ensembles of mixed random matrices.
In this paper, we numerically solve the thermodynamic Bethe-ansatz coupled equations for a one-di... more In this paper, we numerically solve the thermodynamic Bethe-ansatz coupled equations for a one-dimensional Hubbard model at finite temperature and obtain the second order thermodynamics properties, such as the specific heat, compressibility, and susceptibility. We find that these three quantities could embody the phase transitions of the system, from the vacuum state to the metallic state, from the metallic state to the Mott-insulating phase, from the Mott-insulating phase to the metallic state, and from the metallic state to the band-insulating phase. With the increase of temperature, the thermal fluctuation overwhelms the quantum fluctuations and the phase transition points disappear due to the destruction of the Mott-insulating phase. But in the case of the strong interaction strength, the Mott-insulating phase is robust, embodying the compressibility. Furthermore, we study the thermodynamic properties of the inhomogeneous Hubbard model with trapping potential. Making use of the ...
After a quench of transverse field, the asymptotic long-time state of Ising model displays a tran... more After a quench of transverse field, the asymptotic long-time state of Ising model displays a transition from a ferromagnetic phase to a paramagnetic phase as the post-quench field strength increases, which is revealed by the vanishing of the order parameter defined as the averaged magnetization over time. We estimate the critical behavior of the magnetization at this nonequilibrium phase transition by using mean-field approximation. In the vicinity of the critical field, the magnetization vanishes as the inverse of a logarithmic function, which is significantly distinguished from the critical behavior of order parameter at the corresponding equilibrium phase transition, i.e. a power-law function.
In the framework of the tight binding approximation, we study a non-interacting model on the thre... more In the framework of the tight binding approximation, we study a non-interacting model on the three-component dice lattice with real nearest-neighbor and complex next-nearest-neighbor hopping subjected to $\Lambda$- or V-type sublattice potentials. By analyzing the dispersions of corresponding energy bands, we find that the system undergoes a metal-insulator transition which can be modulated not only by the Fermi energy but also the tunable extra parameters. Furthermore, rich topological phases, including the ones with high Hall plateau, are uncovered by calculating the associated band's Chern number. Besides, we also analyze the edge-state spectra and discuss the correspondence between Chern numbers and the edge states by the principle of bulk-edge correspondence.
arXiv: Disordered Systems and Neural Networks, 2016
We study a one-dimensional quasiperiodic system described by the off-diagonal Aubry-Andr\'{e}... more We study a one-dimensional quasiperiodic system described by the off-diagonal Aubry-Andr\'{e} model and investigate its phase diagram by using the symmetry and the multifractal analysis. It was shown in a recent work ({\it Phys. Rev. B} {\bf 93}, 205441 (2016)) that its phase diagram was divided into three regions, dubbed the extended, the topologically-nontrivial localized and the topologically-trivial localized phases, respectively. Out of our expectation, we find an additional region of the extended phase which can be mapped into the original one by a symmetry transformation. More unexpectedly, in both "localized" phases, most of the eigenfunctions are neither localized nor extended. Instead, they display critical features, that is, the minimum of the singularity spectrum is in a range $0<\gamma_{min}<1$ instead of $0$ for the localized state or $1$ for the extended state. Thus, a mixed phase is found with a mixture of localized and critical eigenfunctions.
Casimir effects manifests that, the two closely paralleled plates, generally produce a macroscopi... more Casimir effects manifests that, the two closely paralleled plates, generally produce a macroscopic attractive force due to the quantum vacuum fluctuations of the electromagnetic fields. The derivation of the force requires an {\it artificial} regulator by removing the divergent summation. By including naturally a spectrum density factor, based on the observation that an incomplete eigenvectors of observable, such as the eigenstates for the photons in the free field, can form a complete set of eigenvectors by introducing a unique spectrum transformation, an alternative way is presented to rederive the force, without using a regulator. As a result, the Casimir forces are obtained with the first term $-\pi^2 \hbar c/(240 a^4)$ attractive, and the second one, $-\pi^4 \hbar c^3 \sigma^2/(1008 a^6)$, also attractive but smaller, with $a$ the plate separation, and $\sigma$ a to-be-determined small constant number in the spectrum density factor.
We investigate the quench dynamics of a one-dimensional incommensurate lattice described by the A... more We investigate the quench dynamics of a one-dimensional incommensurate lattice described by the Aubry-André model by a sudden change of the strength of incommensurate potential ∆ and unveil that the dynamical signature of localization-delocalization transition can be characterized by the occurrence of zero points in the Loschmit echo. For the quench process with quenching taking place between two limits of ∆ = 0 and ∆ = ∞, we give analytical expressions of the Loschmidt echo, which indicate the existence of a series of zero points in the Loschmidt echo. For a general quench process, we calculate the Loschmidt echo numerically and analyze its statistical behavior. Our results show that if both the initial and post-quench Hamiltonian are in extended phase or localized phase, Loschmidt echo will always be greater than a positive number; however if they locate in different phases, Loschmidt echo can reach nearby zero at some time intervals.
We investigate the nonequilibrium dynamics of the one-dimension Aubry-André-Harper model with p-w... more We investigate the nonequilibrium dynamics of the one-dimension Aubry-André-Harper model with p-wave superconductivity by changing the potential strength with slow and sudden quench. Firstly, we study the slow quench dynamics from the localized phase to the critical phase by linearly decreasing the potential strength V. The localization length is finite and its scaling obeys the Kibble-Zurek mechanism. The results show that the second-order phase transition line shares the same critical exponent zν, giving the correlation length ν = 1 and dynamical exponent z = 1.373 ± 0.023, which are different from the Aubry-André model. Secondly, we also study the sudden quench dynamics between three different phases: localized phase, critical phase, and extended phase. In the limit of V = 0 and V = ∞, we analytically study the sudden quench dynamics via the Loschmidt echo. The results suggest that, if the initial state and the post-quench Hamiltonian are in different phases, the Loschmidt echo vanishes at some time intervals. Furthermore, we found that, if the initial value is in the critical phase, the direction of quenching is the same as one of the two limits mentioned before, and similar behaviors will occur.
With respect to the quantum anomalous Hall effect (QAHE), the detection of topological nontrivial... more With respect to the quantum anomalous Hall effect (QAHE), the detection of topological nontrivial large-Chern-number phases is an intriguing subject. Motivated by recent research on Floquet topological phases, this study proposes a periodic driving protocol to engineer large-Chern-number phases using the QAHE. Herein, spinless ultracold fermionic atoms are studied in a two-dimensional optical dice lattice with nearest-neighbor hopping and a-or V-type sublattice potential subjected to a circular driving force. Results suggest that large-Chern-number phases exist with Chern numbers C = −3, which is consistent with the edge-state quasienergy spectra.
The existence of many-body mobility edges in closed quantum systems has been the focus of intense... more The existence of many-body mobility edges in closed quantum systems has been the focus of intense debate after the emergence of the description of the many-body localization phenomenon. Here we propose that this issue can be settled in experiments by investigating the time evolution of local degrees of freedom, tailored for specific energies and intial states. An interacting model of spinless fermions with exponentially long-ranged tunneling amplitudes, whose non-interacting version known to display single-particle mobility edges, is used as the starting point upon which nearest-neighbor interactions are included. We verify the manifestation of many-body mobility edges by using numerous probes, suggesting that one cannot explain their appearance as merely being a result of finite-size effects.
We study a one-dimensional quasiperiodic system described by the Aubry-André model in the small w... more We study a one-dimensional quasiperiodic system described by the Aubry-André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry-André model are either extended or localized depending on the strength of incommensurate potential V being less or bigger than a critical value Vc, and thus no mobility edge exists. However, it was shown in a recent work that this conclusion does not hold true when the wave vector α of the incommensurate potential is small, and for the system with V < Vc, there exist almost mobility edges at the energy Ec ± , which separate the robustly delocalized states from "almost localized" states. We find that, besides Ec ± , there exist additionally another energy edges E c ′ ± , at which abrupt change of inverse participation ratio occurs. By using the inverse participation ratio and carrying out multifractal analyses, we identify the existence of critical regions among |Ec ± | ≤ |E| ≤ |E c ′ ± | with the almost mobility edges Ec ± and E c ′ ± separating the critical region from the extended and localized regions, respectively. We also study the system with V > Vc, for which all eigenstates are localized states, but can be divided into extended, critical and localized states in their dual space by utilizing the self-duality property of the Aubry-André model.
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