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wanzhou zhang

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Papers by wanzhou zhang

Sublattice extraordinary-log phase and new special point of the antiferromagnetic Potts model

arXiv (Cornell University), Jan 21, 2023

Machine learning of percolation models using graph convolutional neural networks

arXiv (Cornell University), Jul 7, 2022

Machine learning for percolation utilizing auxiliary Ising variables

Physical Review E, 2022

Machine learning for phase transition has received intensive research interest in recent years. H... more Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for machine learning study of the standard percolation as well as a variety of statistical mechanical systems in correlated percolation representations. We demonstrate that unsupervised machine learning is able to accurately locate the percolation threshold, independent of the spatial dimension of system or the type of phase transition, which can be first order or continuous. Moreover, we show that, by neural network machine learning, auxiliary Ising configurations for different universalities can be classified with high confidence level. Our results indicate that the auxiliary Ising mapping method, despite of it simplicity, can advance the application of machine learning in statistical and condensed-matter physics.

Beats and broken-symmetry superfluid on a one dimensional anyon Hubbard model

Phase transitions in a three-dimensional Ising model with cluster weight studied by Monte Carlo simulations

Physical Review E, 2021

A cluster weight Ising model is proposed by introducing an additional cluster weight in the parti... more A cluster weight Ising model is proposed by introducing an additional cluster weight in the partition function of the traditional Ising model. It is equivalent to the O(n) loop model or ncomponent face cubic loop model on the two-dimensional lattice, but on the three-dimensional lattice, it is still not very clear whether or not these models have the same universality. In order to simulate the cluster weight Ising model and search for new universality class, we apply a cluster algorithm, by combining the color-assignation and the Swendsen-Wang methods. The dynamical exponent for the absolute magnetization is estimated to be z = 0.45(3) at n = 1.5, consistent with that by the traditional Swendsen-Wang methods. The numerical estimation of the thermal exponent yt and magnetic exponent ym, show that the universalities of the two models on the three dimensional lattice are different. We obtain the global phase diagram containing paramagnetic and ferromagnetic phases. The phase transition between the two phases are second order at 1 ≤ n < nc and first order at n ≥ nc, where nc ≈ 2. The scaling dimension yt equals to the system dimension d when the first order transition occurs. Our results are helpful in the understanding of some traditional statistical mechanics models.

Phase transitions in 3D Ising model with cluster weight by Monte Carlo method

Ziyang Wang, 2 Le Feng, Wanzhou Zhang, 2, ∗ and Chengxiang Ding † Key Laboratory of Quantum Infor... more Ziyang Wang, 2 Le Feng, Wanzhou Zhang, 2, ∗ and Chengxiang Ding † Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, PR China College of Physics and Optoelectronics, Taiyuan University of Technology, Shanxi 030024, China School of Science and Engineering of Mathematics and Physics, Anhui University of Technology, Maanshan 243002, China (Dated: July 23, 2021)

Beats, broken-symmetry superfluid on a one dimensional anyon Hubbard model

arXiv: Quantum Gases, 2015

By using the density matrix renormalization group and mean field methods, the anyon Hubbard model... more By using the density matrix renormalization group and mean field methods, the anyon Hubbard model is studied systematically on a one dimensional lattice. The model can be expressed as a Bose-Hubbard model with a density-dependent-phase term. When the phase angle is $\theta=0$ or $\theta=\pi$, the model will be equivalent to boson and pseudo fermion models, respectively. In the mean field frame, we find a broken-symmetry superfluid (BSF), in which the $b^{\dagger}(b)$ operators on the nearest neighborhood sites have exactly opposite directions and behave like a directed oscillation pattern. By the density matrix reorganization group method, in the broken-symmetry superfluid, both the real and imaginary parts of the correlation $b^{\dagger}_ib_{i+r}$ behave according to a {\it beat phenomenon} with $0<\theta<\pi$ in the form $C_0e^{i k r}(-1)^{r}$ or behave like waves with different wavelengths in the form $C_0e^{i k r}$. The distributions of the broken-symmetry superfluid phase...

Unsupervised learning of topological phase transitions using the Calinski-Harabaz index

Physical Review Research, 2021

Machine learning methods have been recently applied to learning phases of matter and transitions ... more Machine learning methods have been recently applied to learning phases of matter and transitions between them. Of particular interest is the topological phase transition, such as in the XY model, whose critical points can be difficult to be obtained by using unsupervised learning such as the principal component analysis. Recently, authors of [Nature Physics 15,790 (2019)] employed the diffusion map method for identifying topological orders and were able to determine the Berezinskii-Kosterlitz-Thouless (BKT) phase transition of the XY model, specifically via the intersection of the average cluster distanceD and the within-cluster dispersion parameterσ (when the different clusters vary from separation to mixing together). However, sometimes it is not easy to find the intersection ifD orσ does not change too much due to topological constraint. In this work, we propose to use the Calinski-Harabaz (ch) index, defined roughly as the ratioD/σ, to determine the critical points, at which the ch index reaches a maximum or minimum value, or jumps sharply. We examine the ch index in several statistical models, including ones that contain a BKT phase transition. For the Ising model, the peaks of the quantity ch or its components are consistent with the position of the specific heat maximum. For the XY model, both on the square and honeycomb lattices, our results of the ch index show the convergence of the peaks over a range of the parameters ε/ε0 in the Gaussian kernel. We also examine the generalized XY model with q = 2 and q = 8 and study the phase transition using the fractional 1/2-vortex or 1/8-vortex constraint respectively. The global phase diagram can be obtained by our method, which does not use the label of configuration needed by supervised learning, nor a crossing from two curvesD andσ. Our method is thus useful to both topological and non-topological phase transitions and can achieve accuracy as good as supervised learning methods previously used in these models, and may be used for searching phases from experimental data.

Supersolid and pair correlations of the extended Jaynes-Cummings-Hubbard model on triangular lattices

Physical Review A, 2019

We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladd... more We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to two-dimensional triangular lattices, we present evidence for the emergence of a light supersolid in this case also.

Machine learning of phase transitions in the percolation andXYmodels

Physical Review E, 2019

Off-site trimer superfluid on a one-dimensional optical lattice

Chinese Physics B, 2017

The Bose-Hubbard model with an effective off-site three-body tunneling, characterized by jumps to... more The Bose-Hubbard model with an effective off-site three-body tunneling, characterized by jumps towards one another, between one atom on a site and a pair atoms on the neighborhood site, is studied systematically on a one-dimensional lattice, by using the density matrix renormalization group method. The off-site trimer superfluid, condensing at momentum k = 0, emerges in the softcore Bose-Hubbard model but it disappears in the hardcore Bose-Hubbard model. Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from [Phys. Rev. A 81, 011601(R) (2010)] is stable in the thermodynamic limit. The off-site trimer superfluid phase, the partially off-site trimer superfluid phase and the Mott insulator phase are found, as well as interesting phase transitions, such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase. Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.

The coupled electromagnetic field effects on quantum transport in an electrically modulated graphene

Physics Letters A, 2016

Abstract Recent experiments have revealed that the periodic graphene ripples can cause a periodic... more Abstract Recent experiments have revealed that the periodic graphene ripples can cause a periodic potential. Motivated by this, we have explored the electromagnetic field effects on the transport of graphene subjected to an electric periodic potential. Comparing with recently obtained results for magnetically modulated graphene, we also find an abrupt disappearance of oscillations in the magnetoconductivity at γ e = 1 , and in a strong magnetic field, the Shubnikov–de Haas oscillations on it are superimposed on the Weiss oscillations. However, these oscillations with the electric and magnetic modulations have a π phase shift. Our results should be valuable for electronic applications of graphene.

Ground-state properties of the one-dimensional unconstrained pseudo-anyon Hubbard model

Physical Review A, 2017

We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without the presence of a... more We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without the presence of a three-body hardcore constraint. In particular, for the pseudo-fermion limit of a large statistical angle θ ≈ π, we observe a wealth of exotic properties including a first order transition between different superfluid phases and a two-component partially paired phase for large fillings without need of an additional three-body hardcore constraint. In this limit, we analyze the effect of an induced hardcore constraint, which leads to the stabilization of superfluid ground states for vanishing or even small attractive on-site interactions. For finite statistical angles, we study the unconventional broken-symmetry superfluid peaked at a finite momentum, resulting in an interesting beat phenomenon of single particle correlation functions. We show how some features of various ground state phases, including an analog of the partially paired phase in the pseudo-fermion limit, may be reproduced in a naive mean field frame.

Percolation of the site random-cluster model by Monte Carlo method

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

We propose a site random-cluster model by introducing an additional cluster weight in the partiti... more We propose a site random-cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the Swendsen-Wang methods to design a highly efficient cluster algorithm with a small critical slowing-down phenomenon. To verify whether or not it is consistent with the bond random-cluster model, we measure several quantities, such as the wrapping probability R_{e}, the percolating cluster density P_{∞}, and the magnetic susceptibility per site χ_{p}, as well as two exponents, such as the thermal exponent y_{t} and the fractal dimension y_{h} of the percolating cluster. We find that for different exponents of cluster weight q=1.5, 2, 2.5, 3, 3.5, and 4, the numerical estimation of the exponents y_{t} and y_{h} are consistent with the theoretical values. The universalities of the site random-cluster model and the bond random-cluster model are completely identi...

Critical properties of the Baxter-Wu model on the Union-Jack lattice

As a generalization of the Baxter-Wu model, we numerically study the Ising model with triplet int... more As a generalization of the Baxter-Wu model, we numerically study the Ising model with triplet interactions on the Union-Jack lattice, which we call as Union-Jack Baxter-Wu model. By means of finite-size scaling analysis based on Monte Carlo simulations and transfer matrix calculations, we numerically determine the critical exponents (or scaling dimensions) and the central charge of the model. The critical exponents studied include $y_t$, $y_h$, $y_{h1}$, and $y_{h2}$, where $y_t$ governs the critical behavior of the correlation length, $y_{h}$ governs the critical behavior of the magnetization of the whole lattice, $y_{h1}$ and $y_{h2}$ govern respectively the critical behaviors of the magnetizations on the two sublattices of the Union-Jack lattice. For the critical exponents $y_t$, $y_{h1}$, $y_{h2}$, and the critical points of the model, our numerical estimations coincide with the exact solutions. For the critical exponent $y_h$ and the central charge $c$, as we know, there is no ...

Trimer superfluid and supersolid on two-dimensional optical lattices

Physical Review A, 2015

Trimer superfluid induced by photoassocation on the state-dependent optical lattice

Physical Review A, 2014

Critical properties of the Hintermann-Merlini model

Physical Review E, 2013

Many critical properties of the Hintermann-Merlini model are known exactly through the mapping to... more Many critical properties of the Hintermann-Merlini model are known exactly through the mapping to the eight-vertex model. Wu [J. Phys. C 8, 2262 (1975)] calculated the spontaneous magnetizations of the model on two sublattices by relating them to the conjectured spontaneous magnetization and polarization of the eight-vertex model, respectively. The latter conjecture remains unproved. In this paper, we numerically study the critical properties of the model by means of a finite-size scaling analysis based on transfer matrix calculations and Monte Carlo simulations. All analytic predictions for the model are confirmed by our numerical results. The central charge c = 1 is found for critical manifold investigated. In addition, some unpredicted geometry properties of the model are studied. Fractal dimensions of the largest Ising clusters on two sublattices are determined. The fractal dimension of the largest Ising cluster on the sublattice A takes fixed value Da = 1.888(2), while that for sublattice B varies continuously with the parameters of the model.

Pair supersolid with atom-pair hopping on the state-dependent triangular lattice

Physical Review B, 2013

We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in... more We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of largescale Quantum Monte Carlo simulations, the ground-state phase diagram are studied. We find a continuous transition between the atomic superfluid phase and the pair superfluid when the ratio of the atomic hopping and the atom-pair hopping is adapted. We then focus on the interplay among the atom-pair hopping, the on-site repulsion and the nearest-neighbor repulsion. With on-site repulsion present, we observe first order transitions between the Mott Insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/3, 1 and 4/3-filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasi hardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. The transition between the pair supersolid and the pair superfluid is first order, except for the particle-hole symmetric point. We compare the results with those obtained by means of mean-field analysis.

Effects of edge disorder in nanoscale antiferromagnetic clusters

Physical Review B, 2010

Sublattice extraordinary-log phase and new special point of the antiferromagnetic Potts model

arXiv (Cornell University), Jan 21, 2023

Machine learning of percolation models using graph convolutional neural networks

arXiv (Cornell University), Jul 7, 2022

Machine learning for percolation utilizing auxiliary Ising variables

Physical Review E, 2022

Machine learning for phase transition has received intensive research interest in recent years. H... more Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for machine learning study of the standard percolation as well as a variety of statistical mechanical systems in correlated percolation representations. We demonstrate that unsupervised machine learning is able to accurately locate the percolation threshold, independent of the spatial dimension of system or the type of phase transition, which can be first order or continuous. Moreover, we show that, by neural network machine learning, auxiliary Ising configurations for different universalities can be classified with high confidence level. Our results indicate that the auxiliary Ising mapping method, despite of it simplicity, can advance the application of machine learning in statistical and condensed-matter physics.

Beats and broken-symmetry superfluid on a one dimensional anyon Hubbard model

Phase transitions in a three-dimensional Ising model with cluster weight studied by Monte Carlo simulations

Physical Review E, 2021

A cluster weight Ising model is proposed by introducing an additional cluster weight in the parti... more A cluster weight Ising model is proposed by introducing an additional cluster weight in the partition function of the traditional Ising model. It is equivalent to the O(n) loop model or ncomponent face cubic loop model on the two-dimensional lattice, but on the three-dimensional lattice, it is still not very clear whether or not these models have the same universality. In order to simulate the cluster weight Ising model and search for new universality class, we apply a cluster algorithm, by combining the color-assignation and the Swendsen-Wang methods. The dynamical exponent for the absolute magnetization is estimated to be z = 0.45(3) at n = 1.5, consistent with that by the traditional Swendsen-Wang methods. The numerical estimation of the thermal exponent yt and magnetic exponent ym, show that the universalities of the two models on the three dimensional lattice are different. We obtain the global phase diagram containing paramagnetic and ferromagnetic phases. The phase transition between the two phases are second order at 1 ≤ n < nc and first order at n ≥ nc, where nc ≈ 2. The scaling dimension yt equals to the system dimension d when the first order transition occurs. Our results are helpful in the understanding of some traditional statistical mechanics models.

Phase transitions in 3D Ising model with cluster weight by Monte Carlo method

Ziyang Wang, 2 Le Feng, Wanzhou Zhang, 2, ∗ and Chengxiang Ding † Key Laboratory of Quantum Infor... more Ziyang Wang, 2 Le Feng, Wanzhou Zhang, 2, ∗ and Chengxiang Ding † Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, PR China College of Physics and Optoelectronics, Taiyuan University of Technology, Shanxi 030024, China School of Science and Engineering of Mathematics and Physics, Anhui University of Technology, Maanshan 243002, China (Dated: July 23, 2021)

Beats, broken-symmetry superfluid on a one dimensional anyon Hubbard model

arXiv: Quantum Gases, 2015

By using the density matrix renormalization group and mean field methods, the anyon Hubbard model... more By using the density matrix renormalization group and mean field methods, the anyon Hubbard model is studied systematically on a one dimensional lattice. The model can be expressed as a Bose-Hubbard model with a density-dependent-phase term. When the phase angle is $\theta=0$ or $\theta=\pi$, the model will be equivalent to boson and pseudo fermion models, respectively. In the mean field frame, we find a broken-symmetry superfluid (BSF), in which the $b^{\dagger}(b)$ operators on the nearest neighborhood sites have exactly opposite directions and behave like a directed oscillation pattern. By the density matrix reorganization group method, in the broken-symmetry superfluid, both the real and imaginary parts of the correlation $b^{\dagger}_ib_{i+r}$ behave according to a {\it beat phenomenon} with $0<\theta<\pi$ in the form $C_0e^{i k r}(-1)^{r}$ or behave like waves with different wavelengths in the form $C_0e^{i k r}$. The distributions of the broken-symmetry superfluid phase...

Unsupervised learning of topological phase transitions using the Calinski-Harabaz index

Physical Review Research, 2021

Machine learning methods have been recently applied to learning phases of matter and transitions ... more Machine learning methods have been recently applied to learning phases of matter and transitions between them. Of particular interest is the topological phase transition, such as in the XY model, whose critical points can be difficult to be obtained by using unsupervised learning such as the principal component analysis. Recently, authors of [Nature Physics 15,790 (2019)] employed the diffusion map method for identifying topological orders and were able to determine the Berezinskii-Kosterlitz-Thouless (BKT) phase transition of the XY model, specifically via the intersection of the average cluster distanceD and the within-cluster dispersion parameterσ (when the different clusters vary from separation to mixing together). However, sometimes it is not easy to find the intersection ifD orσ does not change too much due to topological constraint. In this work, we propose to use the Calinski-Harabaz (ch) index, defined roughly as the ratioD/σ, to determine the critical points, at which the ch index reaches a maximum or minimum value, or jumps sharply. We examine the ch index in several statistical models, including ones that contain a BKT phase transition. For the Ising model, the peaks of the quantity ch or its components are consistent with the position of the specific heat maximum. For the XY model, both on the square and honeycomb lattices, our results of the ch index show the convergence of the peaks over a range of the parameters ε/ε0 in the Gaussian kernel. We also examine the generalized XY model with q = 2 and q = 8 and study the phase transition using the fractional 1/2-vortex or 1/8-vortex constraint respectively. The global phase diagram can be obtained by our method, which does not use the label of configuration needed by supervised learning, nor a crossing from two curvesD andσ. Our method is thus useful to both topological and non-topological phase transitions and can achieve accuracy as good as supervised learning methods previously used in these models, and may be used for searching phases from experimental data.

Supersolid and pair correlations of the extended Jaynes-Cummings-Hubbard model on triangular lattices

Physical Review A, 2019

We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladd... more We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to two-dimensional triangular lattices, we present evidence for the emergence of a light supersolid in this case also.

Machine learning of phase transitions in the percolation andXYmodels

Physical Review E, 2019

Off-site trimer superfluid on a one-dimensional optical lattice

Chinese Physics B, 2017

The Bose-Hubbard model with an effective off-site three-body tunneling, characterized by jumps to... more The Bose-Hubbard model with an effective off-site three-body tunneling, characterized by jumps towards one another, between one atom on a site and a pair atoms on the neighborhood site, is studied systematically on a one-dimensional lattice, by using the density matrix renormalization group method. The off-site trimer superfluid, condensing at momentum k = 0, emerges in the softcore Bose-Hubbard model but it disappears in the hardcore Bose-Hubbard model. Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from [Phys. Rev. A 81, 011601(R) (2010)] is stable in the thermodynamic limit. The off-site trimer superfluid phase, the partially off-site trimer superfluid phase and the Mott insulator phase are found, as well as interesting phase transitions, such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase. Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.

The coupled electromagnetic field effects on quantum transport in an electrically modulated graphene

Physics Letters A, 2016

Abstract Recent experiments have revealed that the periodic graphene ripples can cause a periodic... more Abstract Recent experiments have revealed that the periodic graphene ripples can cause a periodic potential. Motivated by this, we have explored the electromagnetic field effects on the transport of graphene subjected to an electric periodic potential. Comparing with recently obtained results for magnetically modulated graphene, we also find an abrupt disappearance of oscillations in the magnetoconductivity at γ e = 1 , and in a strong magnetic field, the Shubnikov–de Haas oscillations on it are superimposed on the Weiss oscillations. However, these oscillations with the electric and magnetic modulations have a π phase shift. Our results should be valuable for electronic applications of graphene.

Ground-state properties of the one-dimensional unconstrained pseudo-anyon Hubbard model

Physical Review A, 2017

We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without the presence of a... more We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without the presence of a three-body hardcore constraint. In particular, for the pseudo-fermion limit of a large statistical angle θ ≈ π, we observe a wealth of exotic properties including a first order transition between different superfluid phases and a two-component partially paired phase for large fillings without need of an additional three-body hardcore constraint. In this limit, we analyze the effect of an induced hardcore constraint, which leads to the stabilization of superfluid ground states for vanishing or even small attractive on-site interactions. For finite statistical angles, we study the unconventional broken-symmetry superfluid peaked at a finite momentum, resulting in an interesting beat phenomenon of single particle correlation functions. We show how some features of various ground state phases, including an analog of the partially paired phase in the pseudo-fermion limit, may be reproduced in a naive mean field frame.

Percolation of the site random-cluster model by Monte Carlo method

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

We propose a site random-cluster model by introducing an additional cluster weight in the partiti... more We propose a site random-cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the Swendsen-Wang methods to design a highly efficient cluster algorithm with a small critical slowing-down phenomenon. To verify whether or not it is consistent with the bond random-cluster model, we measure several quantities, such as the wrapping probability R_{e}, the percolating cluster density P_{∞}, and the magnetic susceptibility per site χ_{p}, as well as two exponents, such as the thermal exponent y_{t} and the fractal dimension y_{h} of the percolating cluster. We find that for different exponents of cluster weight q=1.5, 2, 2.5, 3, 3.5, and 4, the numerical estimation of the exponents y_{t} and y_{h} are consistent with the theoretical values. The universalities of the site random-cluster model and the bond random-cluster model are completely identi...

Critical properties of the Baxter-Wu model on the Union-Jack lattice

As a generalization of the Baxter-Wu model, we numerically study the Ising model with triplet int... more As a generalization of the Baxter-Wu model, we numerically study the Ising model with triplet interactions on the Union-Jack lattice, which we call as Union-Jack Baxter-Wu model. By means of finite-size scaling analysis based on Monte Carlo simulations and transfer matrix calculations, we numerically determine the critical exponents (or scaling dimensions) and the central charge of the model. The critical exponents studied include $y_t$, $y_h$, $y_{h1}$, and $y_{h2}$, where $y_t$ governs the critical behavior of the correlation length, $y_{h}$ governs the critical behavior of the magnetization of the whole lattice, $y_{h1}$ and $y_{h2}$ govern respectively the critical behaviors of the magnetizations on the two sublattices of the Union-Jack lattice. For the critical exponents $y_t$, $y_{h1}$, $y_{h2}$, and the critical points of the model, our numerical estimations coincide with the exact solutions. For the critical exponent $y_h$ and the central charge $c$, as we know, there is no ...

Trimer superfluid and supersolid on two-dimensional optical lattices

Physical Review A, 2015

Trimer superfluid induced by photoassocation on the state-dependent optical lattice

Physical Review A, 2014

Critical properties of the Hintermann-Merlini model

Physical Review E, 2013

Many critical properties of the Hintermann-Merlini model are known exactly through the mapping to... more Many critical properties of the Hintermann-Merlini model are known exactly through the mapping to the eight-vertex model. Wu [J. Phys. C 8, 2262 (1975)] calculated the spontaneous magnetizations of the model on two sublattices by relating them to the conjectured spontaneous magnetization and polarization of the eight-vertex model, respectively. The latter conjecture remains unproved. In this paper, we numerically study the critical properties of the model by means of a finite-size scaling analysis based on transfer matrix calculations and Monte Carlo simulations. All analytic predictions for the model are confirmed by our numerical results. The central charge c = 1 is found for critical manifold investigated. In addition, some unpredicted geometry properties of the model are studied. Fractal dimensions of the largest Ising clusters on two sublattices are determined. The fractal dimension of the largest Ising cluster on the sublattice A takes fixed value Da = 1.888(2), while that for sublattice B varies continuously with the parameters of the model.

Pair supersolid with atom-pair hopping on the state-dependent triangular lattice

Physical Review B, 2013

We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in... more We systematically study an extended Bose-Hubbard model with atom hopping and atom-pair hopping in the presence of a three-body constraint on the triangular lattice. By means of largescale Quantum Monte Carlo simulations, the ground-state phase diagram are studied. We find a continuous transition between the atomic superfluid phase and the pair superfluid when the ratio of the atomic hopping and the atom-pair hopping is adapted. We then focus on the interplay among the atom-pair hopping, the on-site repulsion and the nearest-neighbor repulsion. With on-site repulsion present, we observe first order transitions between the Mott Insulators and pair superfluid driven by the pair hopping. With the nearest-neighbor repulsion turning on, three typical solid phases with 2/3, 1 and 4/3-filling emerge at small atom-pair hopping region. A stable pair supersolid phase is found at small on-site repulsion. This is due to the three-body constraint and the pair hopping, which essentially make the model a quasi hardcore boson system. Thus the pair supersolid state emerges basing on the order-by-disorder mechanism, by which hardcore bosons avoid classical frustration on the triangular lattice. The transition between the pair supersolid and the pair superfluid is first order, except for the particle-hole symmetric point. We compare the results with those obtained by means of mean-field analysis.

Effects of edge disorder in nanoscale antiferromagnetic clusters

Physical Review B, 2010