arXiv subjects

Wanzhou Zhang

Publications and source records attributed to Wanzhou Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Logarithmic scaling correction in quench dynamics of the J1-J2 Potts model

In conventional quench dynamics governed by the Kibble-Zurek mechanism (KZM), the defect density generally decays as a pure power law of the quench rate. However, the KZM scaling of the two-dimensional (2D) XY model with topological phase transitions features prominent logarithmic corrections. Nevertheless, it remains unclear whether such logarithmic scaling corrections emerge in discrete-spin systems that host two successive topological phase transitions under thermal quenches. This work investigates the J1-J2 antiferromagnetic Potts model and constructs its equilibrium phase diagram. Based on the temperature ranges of the paramagnetic phase, quasi-long-range ordered (QLRO) phase, long-range ordered phase, and zero-temperature ground state, we design four quench protocols with distinct temperature intervals. Our results demonstrate that quenches terminating in the QLRO phase exhibit logarithmically corrected KZM scaling of the excess energy density, consistent with the dynamical universality class of the 2D XY model. In contrast, quenches ending in the LRO phase, including both finite-temperature and zero-temperature protocols, follow conventional power-law scaling. Our results clearly uncover the characteristic scaling corrections of the J1-J2 Potts model and offer theoretical guidance for future experimental investigations of KZM via photonic simulation platforms.

cond-mat.stat-mech↗

arXiv2026

Local supersolid in moir\'e modulated Bose-Hubbard model using density-matrix renormalization group method

The search and characterization of supersolid phases remain a central topic in condensed matter physics. Inspired by the experimental discovery of local superfluid and insulating phases in two-dimensional moir\'e optical lattices [Meng et al., Nature 615, 231 (2023)], we systematically explore the emergence of a local supersolid ($l$SS) phase in a one-dimensional Bose-Hubbard model subjected to a moir\'e potential, using the density-matrix renormalization group method. We impose a maximum site occupation $n_{\rm max}=2$ to realize the soft-core boson constraint. In the absence of nearest-neighbor repulsion, we identify the conventional superfluid, local superfluid, Mott insulator, and moir\'e-induced insulator phases. When the nearest-neighbor repulsion is turned on, the $l$SS phase emerges in the strong-moir\'e regime. This phase is uniquely characterized by three key signatures: (i) coexisting local staggered density order and local off-diagonal coherence within isolated moir\'e supercells; (ii) exponentially decaying global off-diagonal correlations; and (iii) a vanishing global structure factor in the thermodynamic limit, while the local structure factor remains finite. These features clearly distinguish the $l$SS from the conventional global supersolid (SS) phase, which exhibits algebraic correlations and a finite global structure factor. Our results provide a complete microscopic picture of local quantum phases in moir\'e lattices and offer clear experimental observables for detecting $l$SS states with ultracold atoms.

cond-mat.quant-gas↗

arXiv2026

Emergent critical phases of the Ashkin-Teller model on the Union-Jack Lattice

The Ashkin-Teller (AT) model is a classic spin model in statistical mechanics. For traditional homogeneous lattices like triangular and kagome lattices, even when frustration exists, the model only has one ferromagnetic-paramagnetic critical line in the $J>0$ and $K<0$ region. However, in this paper, for the Union Jack lattice, where the lattice coordination numbers are 4, 8, and 8 and which also contains a large number of small triangular units, using Metropolis Monte Carlo method, we find that, the critical line of the AT model splits into two Berezinskii-Kosterlitz-Thouless(BKT) boundaries, and a critical phase emerges in the intermediate region. This phenomenon is the combined result of frustration, lattice inhomogeneity and the two coupled spin degrees of freedom inherent to the AT model. In detail, the novel critical phase characterized by a power-law decay of magnetization with system size, where the correlation length ratio $\xi/L$ remains finite even in the thermodynamic limit. We also introduce the susceptibility $\widetilde{\chi} = \text{d}\langle m \rangle /\text{d}J$ as a key probe, and through this probe, pseudo-critical points $J_c(L)$ are observed to scale proportionally to $(\ln L)^{-2}$, a behavior consistent with BKT criticality. Since superfluids, superconductors, and supersolids all possess quasi-long-range order and fall into the category of critical phases, our results could also inspire the exploration of such quantum phases.

cond-mat.stat-mech↗

arXiv2026

Phase transitions and crtical exponents in the six-vertex model on kagome lattices

Inspired by the experimental realization of direct kagome spin ice [Yue et al., Nat. Nanotechnol. 19, 1101 (2024)], the theoretical six-vertex model on the kagome lattice is systematically simulated using the directed loop Monte Carlo method. Four distinct vortex lattice phases are identified: (i) antiferromagnetic leg states and vortex lattice order on both triangular and honeycomb faces, with a winding number $k=1$. (ii) ferromagnetic leg states and vortex lattice order on both types of faces, with $k=-2$ on the honeycomb faces and $k=1$ on the triangular faces. (iii) paramagnetic leg states and vortex lattice order on the triangular faces with $k=1$; and (iv) paramagnetic leg states and vortex lattice order on the honeycomb faces with $k=1$. As for ferromagnetic to different types of paramagnetic phase, besides the Ising universality class with $y_t=1$, varying critical exponents have also been found with different values of vertex weights. The transition between the third type and fourth type of vortex lattice phases occurs with the new exponent $y_t=1.340(3)$. The third and fourth types of the vortex lattice phase to the vortex disorder phase are found to be of the Berezinskii-Kosterlitz-Thouless type. These findings contribute to the search for and understanding of ice on complex lattices.

cond-mat.stat-mech↗

arXiv2025

Spiral states, first-order transitions and specific heat multipeak phenomenon in $J_1$-$J_2$-$J_3$ Ising model: A Wang-Landau algorithm study

The classical $J_1$-$J_2$-$J_3$ Ising model on the honeycomb lattice is important for understanding frustrated magnetic phenomena in materials such as FePS$_3$ and Ba$_2$CoTeO$_6$, where diverse phases (e.g., striped, zigzag, armchair) and magnetization plateaus have been experimentally observed. To explain the experimental results, previous mean-field studies have explored its thermal phase transitions, identifying armchair phases and striped phases, but their limitations call for more reliable numerical investigations. In this work, we systematically revisit the classical $J_1$-$J_2$-$J_3$ Ising model using the Wang-Landau algorithm. We find that the armchair (AC) phase, previously reported in mean-field and experimental studies, actually coexists with the spiral (SP) phase, with their combined degeneracy reaching 20-fold (4-fold for the AC states and 16-fold for the spiral states). The phase transitions and critical exponents are studied at different interaction values. We observe first-order phase transitions, continuous phase transitions, and even the multipeak phenomenon in frustrated systems. These results clarify the nature of phases and phase transitions in frustrated Ising systems and their exponents, and additionally provide inspiration for experimental efforts to search for the spiral state and specific-heat multipeak phenomenon.

cond-mat.str-el↗

arXiv2025

Dynamics of Baxter-Wu model

Using Monte Carlo simulations, we investigate the dynamical properties of the Baxter-Wu (BW) model under linear quenches. For the linear cooling process, the scaling behavior of the excess defect density in the critical region aligns well with the predictions of the Kibble-Zurek (KZ) mechanism. However, the scaling behavior of the excess defect density after exiting the impulse regime does not follow from a simple interplay between the KZ mechanism and the coarsening dynamics; the system undergoes a decay close to a power-law form with an exponent that is significantly different from the coarsening exponent observed in instantaneous quenching. For the linear heating process, we show that, if the system starts from its ground state, the relevant exponents describing the KZ mechanism are identical to those in the cooling scenario. We find that the system does not directly enter the adiabatic regime after leaving the impulse regime but instead passes through a crossover regime with an exponential decay of the excess defect density. If the initial state is ordered but not the ground state of the system, the defect density exhibits a good scaling behavior, but the relevant exponents do not conform to the predictions of the KZ mechanism.

cond-mat.stat-mech↗

arXiv2025

Tensor network Monte Carlo simulations for the two-dimensional random-bond Ising model

Disordered lattice spin systems are crucial in both theoretical and applied physics. However, understanding their properties poses significant challenges for Monte Carlo simulations. In this work, we investigate the two-dimensional random-bond Ising model using the recently proposed Tensor Network Monte Carlo (TNMC) method. This method generates biased samples from conditional probabilities computed via tensor network contractions and corrects the bias using the Metropolis scheme. Consequently, the proposals provided by tensor networks function as block updates for Monte Carlo simulations. Through extensive numerical experiments, we demonstrate that TNMC simulations can be performed on lattices as large as $1024\times 1024$ spins with moderate computational resources, a substantial increase from the previous maximum size of $64\times 64$ in MCMC. Notably, we observe an almost complete absence of critical slowing down, enabling the efficient collection of unbiased samples and averaging over a large number of random realizations of bond disorders. We successfully pinpoint the multi-critical point along the Nishimori line with significant precision and accurately determined the bulk and surface critical exponents. Our findings suggest that TNMC is a highly efficient algorithm for exploring disordered and frustrated systems in two dimensions.

cond-mat.stat-mech↗

arXiv2024

First-Order Vortex Lattice Melting in Bilayer Ice: A Monte Carlo Method Study

Inspired by the stable bilayer water ice grown in the laboratory (Nature 577, 60, 2020), we propose a model representing water ice as a two-layer six-vertex model. Using the loop update Monte Carlo method, we unveil meaningful findings. While the square lattice six-vertex model exhibits an antiferromagnetic to disordered phase transition known as the Berezinskii-Kosterlitz-Thouless transition, we observe a different scenario for the bilayer six-vertex model, where the transition type transforms into an Ising transition. We discover the emergence of vortices in the disordered phase, and to stabilize them, vortex excitation is induced. This leads to the presence of distinct 1/2 filling and 2/3 filling vortex lattice phases. More importantly, we identify the phase transitions between the vortex lattice phase and the disordered phase, as well as between the 1/2 and 2/3 vortex lattices, as being of first order. We also propose an experimental scheme for realizing a two-layer six-vertex model based on the artificial ice of particles in a double well trap array. Our findings provide valuable insight into the nature of phase transitions occurring in layered water ice and artificial spin ice systems in experimental setups.

cond-mat.stat-mech↗

arXiv2024

Emergent topological ordered phase for the Ising-XY Model revealed by cluster-updating Monte-Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72, 053604 (2005)] and [arXiv:0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent results. Furthermore, we observe first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The results are useful to help cold atom experiments explore the half-vortex topological phase.

cond-mat.quant-gas↗

arXiv2023

Unsupervised machine learning for identifying phase transition using two-times clustering

In recent years, developing unsupervised machine learning for identifying phase transition is a research direction. In this paper, we introduce a two-times clustering method that can help select perfect configurations from a set of degenerate samples and assign the configuration with labels in a manner of unsupervised machine learning. These perfect configurations can then be used to train a neural network to classify phases. The derivatives of the predicted classification in the phase diagram, show peaks at the phase transition points. The effectiveness of our method is tested for the Ising, Potts, and Blume-Capel models. By using the ordered configuration from two-times clustering, our method can provide a useful way to obtain phase diagrams.

cond-mat.dis-nn↗

arXiv2023

Machine learning of percolation models using graph convolutional neural networks

Percolation is an important topic in climate, physics, materials science, epidemiology, finance, and so on. Prediction of percolation thresholds with machine learning methods remains challenging. In this paper, we build a powerful graph convolutional neural network to study the percolation in both supervised and unsupervised ways. From a supervised learning perspective, the graph convolutional neural network simultaneously and correctly trains data of different lattice types, such as the square and triangular lattices. For the unsupervised perspective, combining the graph convolutional neural network and the confusion method, the percolation threshold can be obtained by the "W" shaped performance. The finding of this work opens up the possibility of building a more general framework that can probe the percolation-related phenomenon.

cond-mat.stat-mech↗

arXiv2023

Snake net and balloon force with a neural network for detecting multiple phases

Unsupervised machine learning applied to the study of phase transitions is an ongoing and interesting research direction. The active contour model, also called the snake model, was initially proposed for target contour extraction in two-dimensional images. In order to obtain a physical phase diagram, the snake model with an artificial neural network is applied in an unsupervised learning way by the authors of [Phys.Rev.Lett. 120, 176401(2018)]. It guesses the phase boundary as an initial snake and then drives the snake to convergence with forces estimated by the artificial neural network. In this paper, we extend this unsupervised learning method with one contour to a snake net with multiple contours for the purpose of obtaining several phase boundaries in a phase diagram. For the classical Blume-Capel model, the phase diagram containing three and four phases is obtained. Moreover, to overcome the limitations of the initial position and speed up the movement of the snake, the balloon force decaying with the iteration steps is introduced and applied to the snake net structure. Our method is helpful in determining the phase diagram with multiple phases, using just snapshots of configurations from cold atoms or other experiments without knowledge of the phases.

cond-mat.stat-mech↗

arXiv2023

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

We study the surface criticality of a three-dimensional classical antiferromagnetic Potts model, whose bulk critical behaviors belongs to the XY model because of emergent O(2) symmetry. We find that the surface antiferromagnetic next-nearest neighboring interactions can drive the extraordinary-log phase to the ordinary phase, the transition between the two phases belongs to the universality class of the well-known special transition of the XY model. Further strengthening the surface next-nearest neighboring interactions, the extraordinary-log phase reappears, but the main critical behaviors are dominated on the sublattices of the model; the special point between the ordinary phase and the sublattice extraordinary-log phase belongs to a new universality class.

cond-mat.stat-mech↗

arXiv2022

Machine learning for percolation utilizing auxiliary Ising variables

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.

cond-mat.stat-mech↗

arXiv2021

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

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 $n$-component 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 of the traditional Swendsen-Wang methods. The numerical estimation of the thermal exponent $y_t$ and magnetic exponent $y_m$, 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 $1\leq n< n_c$ and first order at $n\geq n_c$, where $n_c\approx 2$. The scaling dimension $y_t$ 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.

cond-mat.stat-mech↗

arXiv2020

Unsupervised learning of topological phase transitions using Calinski-Harabaz index

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, which can be difficult for unsupervised learning such as the principal component analysis. Recently, authors of [Nature Physics \textbf{15},790 (2019)] employed the diffusion-map method for identifying topological order and were able to determine the BKT phase transition of the XY model, specifically via the intersection of the average cluster distance $\bar{D}$ and the within cluster dispersion $\barσ$ (when the different clusters vary from separation to mixing together). However, sometimes it is not easy to find the intersection if $\bar{D}$ or $\barσ$ does not change too much due to topological constraint. In this paper, we propose to use the Calinski-Harabaz ($ch$) index, defined roughly as the ratio $\bar D/\bar σ$, to determine the critical points, at which the $ch$ index reaches a maximum or minimum value, or jump 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 lattices and honeycomb lattices, our results of the $ch$ index show the convergence of the peaks over a range of the parameters $\varepsilon/\varepsilon_0$ in the Gaussian kernel. We also examine the generalized XY model with $q=2$ and $q=8$ and at the value away from the pure XY limit. 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.

cond-mat.stat-mech↗

arXiv2020

Worm quantum Monte-Carlo study of phase diagram of extended Jaynes-Cummings-Hubbard model

Herein, we study the extended Jaynes-Cummings-Hubbard model mainly by the large-scale worm quantum Monte-Carlo method to check whether or not a light supersolid phase exists in various geometries, such as the one-dimensional chain, square lattices and triangular lattices. To achieve our purpose, the ground state phase diagrams are investigated. For the one-dimensional chain and square lattices, a first-order transition occurs between the superfluid phase and the solid phase and therefore there is no stable supersolid phase existing in these geometries. Interestingly, soliton/beats of the local densities arise if the chemical potential is adjusted in the finite-size chain. However, this soliton-superfluid coexistence can not be considered as a supersolid in the thermodynamic limit. Searching for a light supersolid, we also studied the Jaynes-Cummings-Hubbard model on triangular lattices, and the phase diagrams are obtained. Through measurement of the structural factor, momentum distribution and superfluid stiffness for various system sizes, a supersolid phase exists stably in the triangular lattices geometry and the regime of the supersolid phase is smaller than that of the mean field results. The light supersolid in the Jaynes-Cummings-Hubbard model is attractive because it has superreliance, which is absent in the pure Bose-Hubbard model. We believe the results in this paper could help search for new novel phases in cold-atom experiments

cond-mat.stat-mech↗

arXiv2019

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

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.

cond-mat.quant-gas↗