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 predictio...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 72053604(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 and reliable results.Furthermore,we observed 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 critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.展开更多
The nondivergence of the generalized Gr¨uneisen ratio(GR)at a quantum critical point(QCP)has been proposed to be a universal thermodynamic signature of self-duality.We study how the Kramers–Wannier-type self-dua...The nondivergence of the generalized Gr¨uneisen ratio(GR)at a quantum critical point(QCP)has been proposed to be a universal thermodynamic signature of self-duality.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 transversefield Ising model exhibit different finite-size scaling behaviors in different sectors.This implies that the numerical diagnosis of self-dual QCP requires identification of the proper symmetry sectors.展开更多
We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations,using an efficient cluster algorithm and a finite-size scaling analysis.The critical points and four critical expo...We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations,using an efficient cluster algorithm and a finite-size scaling analysis.The critical points and four critical exponents of the model are determined for several values of n.Two of the exponents are fractal dimensions,which are obtained numerically for the first time.Our results are consistent with the Coulomb gas predictions for the critical O(n) branch for n < 2 and the results obtained by previous transfer matrix calculations.For n=2,we find that the thermal exponent,the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model.These results confirm that the cubic anisotropy is marginal at n=2 but irrelevant for n < 2.展开更多
基金Project supported by the Hefei National Research Center for Physical Sciences at the Microscale (Grant No.KF2021002)the Natural Science Foundation of Shanxi Province,China (Grant Nos.202303021221029 and 202103021224051)+2 种基金the National Natural Science Foundation of China (Grant Nos.11975024,12047503,and 12275263)the Anhui Provincial Supporting Program for Excellent Young Talents in Colleges and Universities (Grant No.gxyq ZD2019023)the National Key Research and Development Program of China (Grant No.2018YFA0306501)。
文摘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 72053604(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 and reliable results.Furthermore,we observed 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 critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.
基金supported by the National Key R&D Program of China(Grant No.2018YFA0305800)the National Natural Science Foundation of China(Grant Nos.12174387 and 11804337)+3 种基金the Strategic Priority Research Program of CAS(Grant No.XDB28000000)the CAS Youth Innovation Promotion Associationsupported by the National Natural Science Foundation of China(Grant Nos.11975024 and 62175001)the Anhui Provincial Supporting Program for Excellent Young Talents in Colleges and Universities(Grant No.gxyq ZD2019023)。
文摘The nondivergence of the generalized Gr¨uneisen ratio(GR)at a quantum critical point(QCP)has been proposed to be a universal thermodynamic signature of self-duality.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 transversefield Ising model exhibit different finite-size scaling behaviors in different sectors.This implies that the numerical diagnosis of self-dual QCP requires identification of the proper symmetry sectors.
基金Project supported by the National Natural Science Foundation of China (Grant No.10675021)the New Century Excellent Talents in University of China,the Natural Science Foundation of Anhui Province of China (Grant No.090416224)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20103402110053)
文摘We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations,using an efficient cluster algorithm and a finite-size scaling analysis.The critical points and four critical exponents of the model are determined for several values of n.Two of the exponents are fractal dimensions,which are obtained numerically for the first time.Our results are consistent with the Coulomb gas predictions for the critical O(n) branch for n < 2 and the results obtained by previous transfer matrix calculations.For n=2,we find that the thermal exponent,the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model.These results confirm that the cubic anisotropy is marginal at n=2 but irrelevant for n < 2.
