ﻻ يوجد ملخص باللغة العربية
We study the quantum phase transition from a super solid phase to a solid phase of rho = 1/2 for the extended Bose-Hubbard model on the honeycomb lattice using first principles Monte Carlo calculations. The motivation of our study is to quantitatively understand the impact of theoretical input, in particular the dynamical critical exponent z, in calculating the critical exponent nu. Hence we have carried out four sets of simulations with beta = 2N^{1/2}, beta = 8N^{1/2}, beta = N/2, and beta = N/4, respectively. Here beta is the inverse temperature and N is the numbers of lattice sites used in the simulations. By applying data collapse to the observable superfluid density rho_{s2} in the second spatial direction, we confirm that the transition is indeed governed by the superfluid-insulator universality class. However we find it is subtle to determine the precise location of the critical point. For example, while the critical chemical potential (mu/V)_c occurs at (mu/V)_c = 2.3239(3) for the data obtained using beta = 2N^{1/2}, the (mu/V)_c determined from the data simulated with beta = N/2 is found to be (mu/V)_c = 2.3186(2). Further, while a good data collapse for rho_{s2}N can be obtained with the data determined using beta = N/4 in the simulations, a reasonable quality of data collapse for the same observable calculated from another set of simulations with beta = 8N^{1/2} can hardly be reached. Surprisingly, assuming z for this phase transition is determined to be 2 first in a Monte Carlo calculation, then a high quality data collapse for rho_{s2}N can be achieved for (mu/V)_c ~ 2.3184 and nu ~ 0.7 using the data obtained with beta = 8N^{1/2}. Our results imply that one might need to reconsider the established phase diagrams of some models if the accurate location of the critical point is crucial in obtaining a conclusion.
Dark states are stationary states of a dissipative, Lindblad-type time evolution with zero von Neumann entropy, therefore representing examples of pure, steady quantum states. Non-equilibrium dynamics featuring a dark state recently gained a lot of a
A Monte Carlo simulation study of the critical and off-critical behavior of the Baxter-Wu model, which belongs to the universality class of the 4-state Potts model, was performed. We estimate the critical temperature window using known analytical res
When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum mani
We study the robustness of a generalized Kitaevs toric code with Z_N degrees of freedom in the presence of local perturbations. For N=2, this model reduces to the conventional toric code in a uniform magnetic field. A quantitative analysis is perform
The problem of finding a microscopic theory of phase transitions across a critical point is a central unsolved problem in theoretical physics. We find a general solution to that problem and present it here for the cases of Bose-Einstein condensation