arXiv subjects

Chengxiang Ding

Publications and source records attributed to Chengxiang Ding.

At least 19 recordsLinked to original sources

arXiv2026

Deconfined Boundary Phase Transition of a Quantum Critical Heisenberg Model

We investigate the boundary phases of a (2+1)-dimensional quantum critical Heisenberg model with a dangling spin chain. By introducing a multispin $Q$-term along the boundary, we drive a continuous boundary transition from an antiferromagnetic (AF) order to a valence-bond solid (VBS) order. Using large-scale quantum Monte Carlo simulations, we locate the critical point at $Q_{c}=0.310(11)$, and obtain the critical exponents at $Q_{c}$, including $y_{s}=0.81(4)$ and the scaling dimensions of AF and VBS order parameters $\Delta_{s}=0.660(15)$ and $\Delta_{v}=0.204(14)$. The weak long-range AF order for $Q<Q_{c}$ is stabilized by quasi-long-range effective interactions mediated by the critical bulk state, while the VBS phase restores the ordinary critical behavior. Our findings highlight the synergy between topological terms and quasi-long-range interactions in low-dimensional quantum many-body systems.

cond-mat.str-el↗

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

Non-commutative Dynamic Approaches to the Kibble-Zurek Scaling Limit with an Initial Gapless Order

Nonequilibrium many-body physics is one of the core problems in modern physics, while the dynamical scaling from a gapless phase to the critical point is a most important challenge with very few knowledge so far. In the driven dynamics with a tuning rate $R$ across the quantum critical point (QCP) of a system with size $L$, the finite-time scaling shows that the square of the order parameter $m^2$ obeys a simple scaling relation $m^2\propto R^{2\beta/\nu r}$ in the Kibble-Zurek (KZ) scaling limit with $RL^r\gg1$. Here, by studying the driven critical dynamics from a gapless ordered phase in the bilayer Heisenberg model, we unveil that the approaches to the scaling region dominated by the KZ scaling limit with $RL^r\gg1$ are {\it non-commutative}: this scaling region is inaccessible for large $R$ and finite medium $L$, while merely accessible for large $L$ and moderately finite $R$. We attribute this to the memory effect induced by the finite-size correction in the gapless ordered phase. This non-commutative property makes $m^2$ still strongly depends on the system size and deviates from $m^2\propto R^{2\beta/\nu r}$ even for large $R$. We further show that a similar correction applies to the imaginary-time relaxation dynamics. Our results establish an essential extension of nonequilibrium scaling theory with a gapless ordered initial state.

cond-mat.str-el↗

arXiv2025

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

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

Continuously varying critical exponents in an exactly solvable long-range cluster XY mode

We investigate a generalized antiferromagnetic cluster XY model in a transverse magnetic field, where long-range interactions decay algebraically with distance. This model can be exactly solvable within a free fermion framework. By analyzing the gap, we explicitly derive the critical exponents $\nu$ and $z$, finding that the relationship $\nu z = 1$ still holds. However, the values of $\nu$ and $z$ depend on the decaying exponent $\alpha$, in contrast to those for the quantum long-range antiferromagnetic Ising chain. To optimize scaling behavior, we verify these critical exponents using correlation functions and fidelity susceptibility, achieving excellent data collapse across various system sizes by adjusting fitting parameters. Finally, we compute the entanglement entropy at the critical point to determine the central charge $c$, and find it also varies with $\alpha$. This study provides insights into the unique effect of long-range cluster interactions on the critical properties of quantum spin systems.

cond-mat.str-el↗

arXiv2024

Universal Quench Dynamics of an Open Quantum System

Taking the quantum Kitaev chain as an example, we have studied the universal dynamical behaviors resulting from quantum criticality under the condition of environmental temperature quench. Our findings reveal that when the quantum parameter is at its critical value, both the excess excitation density at the end of linear quench and the subsequent free relaxation behavior exhibit universal scaling behaviors. The scaling laws observed upon quenching to the zero-temperature quantum critical point and non-zero temperature points exhibit distinct scaling exponents, which are all intimately related to the dynamical critical exponents of the quantum phase transition. Additionally, for the case of linear quench to finite temperatures, we have also discovered an intrinsic universal dynamical behavior that is independent of quantum criticality. Our research offers profound insights into the relationship between quantum criticality and nonequilibrium dynamics from two perspectives: Kibble-Zurek-like scaling behavior and free relaxation dynamics. Notably, the Kibble-Zurek-like scaling behavior in this context differs from the standard Kibble-Zurek mechanism. These two aspects jointly open up a new avenue for us to understand quantum criticality through real-time dynamical behavior, even at finite temperatures.

quant-ph↗

arXiv2023

Dynamical relaxation of a long-range XY chain

We study the universal real-time relaxation behaviors of a long-range quantum XY chain following a quench. Our research includes both the noncritical and critical quench. In the case of noncritical quench, i.e., neither the initial state nor the postquench Hamiltonian is at a critical point of equilibrium phase transition, a quench to the commensurate phase or incommensurate phase gives a scaling of $t^{-3/2}$ or $t^{-1/2}$, respectively, which is the same as the counterpart of the short-range XY model. However, for a quench to the boundary line between the commensurate and incommensurate phases, the scaling law $t^{-\mu}$ may be different from the $t^{-3/4}$ law of the counterpart of the short-range model. More interestingly, the decaying exponent $\mu$ may depend on the choice of the parameters of the postquench Hamiltonian because of the different asymptotic behaviors of the energy spectrum. Furthermore, in certain cases, the scaling behavior may be outside the range of predictions made by the stationary phase approximation, because an inflection point emerges in the energy spectrum. For the critical quench, i.e., the initial state or the postquench Hamiltonian is at a critical point of equilibrium phase transition, the aforementioned scaling law $t^{-\mu}$ may be changed because of the gap-closing property of the energy spectrum of the critical point.

cond-mat.stat-mech↗

arXiv2023

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

Dynamical relaxation behaviors of a critical quench

We study the universal dynamical relaxation behaviors of a quantum XY chain following a quench, paying special attention to the case that the prequenched Hamiltonian, or the postquenched Hamiltonian, or both of them are at critical points of equilibrium quantum phase transitions. In such ``critical quench", we find very interesting real-time dynamical scaling behaviors and the crossover phenomena between them. For a quench from a noncritical point to a critical point, we find that, compared to the noncritical quench, the universal power-law scaling behavior does not change; however, there may be a crossover between the exponential decaying behavior and the power-law scaling. For a quench from a critical point to a noncritical point, the power-law scaling behaviors $t^{-3/2}$ and $t^{-3/4}$ in the noncritical quenches may be changed to $t^{-1}$ and $t^{-1/2}$, respectively. If the prequenched Hamiltonian is set to be a point that is close to but not exactly at a critical point, we find interesting crossover phenomena between different power-law scaling behaviors. We also study the quench from the vicinity of a multicritical point, we find crossover behaviors that are induced by a different mechanism, and new crossover exponent is found. All the results are related to the gap-closing properties of the energy spectrum of the critical points.

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↗

arXiv2023

Quantum criticality of a $\mathbb{Z}_{3}$ symmetric spin chain with long-range interactions

Based on large-scale density matrix renormalization group techniques, we investigate the critical behaviors of quantum three-state Potts chains with long-range interactions. Using fidelity susceptibility as an indicator, we obtain a complete phase diagram of the system. The results show that as the long-range interaction power $\alpha$ increases, the critical points $f_{c}^{*}$ shift towards lower values. In addition, the critical threshold $\alpha_{c}(\approx 1.43$) of the long-range interaction power is obtained for the first time by a non-perturbative numerical method. This indicates that the critical behavior of the system can be naturally divided into two distinct universality classes, namely the long-range ($\alpha \textless \alpha_c$) and short-range ($\alpha \textgreater \alpha_c$) universality classes, qualitatively consistent with the classical $\phi^{3}$ effective field theory. This work provides a useful reference for further research on phase transitions in quantum spin chains with long-range interaction.

cond-mat.str-el↗

arXiv2023

Finite-Size Scaling Theory at a Self-Dual Quantum Critical Point

The nondivergence of the generalized Grüneisen ratio (GR) at a quantum critical point (QCP) has been proposed to be a universal thermodynamic signature of self-duality. In this work, we study how the Kramers-Wannier-type self-duality manifests itself in the finite-size scaling behavior of thermodynamic quantities in the quantum critical regime. While the self-duality cannot be realized as a unitary transformation in the total Hilbert space for the Hamiltonian with the periodic boundary condition, it can be implemented in certain symmetry sectors with proper boundary conditions. Therefore, the GR and the transverse magnetization of the one-dimensional transverse-field Ising model exhibit different finite-size scaling behaviors in different sectors. This implies that the numerical diagnosis of self-dual QCP requires identifying the proper symmetry sectors.

cond-mat.str-el↗

arXiv2022

Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains

Some quantum critical states cannot be smoothly deformed into each other without either crossing some multicritical points or explicitly breaking certain symmetries even if they belong to the same universality class. This brings up the notion of ``symmetry-enriched'' quantum criticality. While recent works in the literature focused on critical states with robust degenerate edge modes, we propose that the conformal boundary condition (b.c.) is a more generic characteristic of such quantum critical states. We show that in two families of quantum spin chains, which generalize the Ising and the three-state Potts models, the quantum critical point between a symmetry-protected topological phase and a symmetry-breaking order realizes a conformal b.c. distinct from the simple Ising and Potts chains. Furthermore, we argue that the conformal b.c. can be derived from the bulk effective field theory, which realizes a novel bulk-boundary correspondence in symmetry-enriched quantum critical states.

cond-mat.str-el↗

arXiv2022

Surface criticality of antiferromagnetic Potts model

We study the three-state antiferromagnetic Potts model on the simple-cubic lattice, paying attention to the surface critical behaviors. When the nearest neighboring interactions of the surface is tuned, we obtain a phase diagram similar to the XY model, owing to the emergent O(2) symmetry of the bulk critical point. For the ordinary transition, we get $y_{h1}=0.780(3)$, $η_\parallel=1.44(1)$, and $η_\perp=0.736(6)$; for the special transition, we get $y_s=0.59(1)$, $y_{h1}=1.693(2)$, $η_\parallel=-0.391(4)$, and $η_\perp=-0.179(5)$; in the extraordinary-log phase, the surface correlation function $C_\parallel(r)$ decays logarithmically, with decaying exponent $q=0.60(2)$, however, the correlation $C_\perp(r)$ still decays algebraically, with critical exponent $η_\perp=-0.442(5)$. If the ferromagnetic next nearest neighboring surface interactions are added, we find two transition points, the first one is a special point between the ordinary phase and the extraordinary-log phase, the second one is a transition between the extraordinary-log phase and the $Z_6$ symmetry-breaking phase, with critical exponent $y_{\rm s}=0.41(2)$. The scaling behaviors of the second transition is very interesting, the surface spin correlation function $C_\parallel(r)$ and the surface squared staggered magnetization at this point decays logarithmically, with exponent $q=0.37(1)$; however, the surface structure factor with the smallest wave vector and the correlation function $C_\perp(r)$ satisfy power-law decaying, with critical exponents $η_\parallel=-0.69(1)$ and $η_\perp=-0.37(1)$, respectively.

cond-mat.stat-mech↗

arXiv2022

Exotic surface behaviors induced by geometrical settings of the two-dimensional dimerized quantum XXZ model

We study the surface behavior of the two-dimensional columnar dimerized quantum antiferromagnetic XXZ model with easy-plane anisotropy, with particular emphasis on the surface critical behaviors of the (2+1)-dimensional quantum critical points of the model that belong to the classical three-dimensional O(2) universality class, for both $S=1/2$ and $S=1$ spins using quantum Monte Carlo simulations. We find completely different surface behaviors on two different surfaces of geometrical settings: the dangling-ladder surface, which is exposed by cutting a row of weak bonds, and the dangling-chain surface, which is formed by cutting a row of strong bonds along the direction perpendicular to the strong bonds of a periodic system. Similar to the Heisenberg limit, we find an ordinary transition on the dangling-ladder surface for both $S=1$ and $S=1/2$ spin systems. However, the dangling-chain surface shows much richer surface behaviors than in the Heisenberg limit. For the $S=1/2$ easy-plane model, at the bulk critical point, we provide evidence supporting an extraordinary surface transition with a long-range order established by effective long-range interactions due to bulk critical fluctuations. The possibility that the state is an extraordinary-log state seems unlikely. For the $S=1$ system, we find surface behaviors similar to that of the three-dimensional classical XY model with sufficiently enhanced surface coupling, suggesting an extraordinary-log state at the bulk critical point.

cond-mat.str-el↗

arXiv2021

Special Transition and Extraordinary Phase on the Surface of a Two-Dimensional Quantum Heisenberg Antiferromagnet

Continuous phase transitions exhibit richer critical phenomena on the surface than in the bulk, because distinct surface universality classes can be realized at the same bulk critical point by tuning the surface interactions. The exploration of surface critical behavior provides a window looking into higher-dimensional boundary conformal field theories. In this work, we study the surface critical behavior of a two-dimensional (2D) quantum critical Heisenberg model by tuning the surface coupling strength, and discover a direct special transition on the surface from the ordinary phase into an extraordinary phase. The extraordinary phase has a long-range antiferromagnetic order on the surface, in sharp contrast to the logarithmic decaying spin correlations in the 3D classical O(3) model. The special transition point has a new set of critical exponents, $y_{s}=0.86(4)$ and $\eta_{\parallel}=-0.33(1)$, which are distinct from the special transition of the classical O(3) model and indicate a new surface universality class of the 3D O(3) Wilson-Fisher theory.

cond-mat.str-el↗

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↗