Superconductivity as a Kosterlitz–Thouless transition in the two-dimensional Hubbard model

We investigate a superconducting Kosterlitz–Thouless transition in the two-dimensional (2D) Hubbard model using auxiliary quantum Monte Carlo method for the ground state. The pair susceptibility is computed for both the attractive and repulsive Hubbard model. The numerical results show that the s-wave pair susceptibility scales as χ  L² for the attractive case, in agreement with previous quantum Monte Carlo studies. The scaling χ  L² also holds for the d-wave pair susceptibility for the repulsive Hubbard model if we adjust the band parameter t′.     

The deconfining phase transition in lattice quantum chromodynamics

We present a large-scale Monte Carlo calculation of the deconfining phase transition temperature in lattice quantum chromodynamics without fermions. Using the Wilson action, the transition temperature as a function of the lattice couplingg is consistent with scaling behavior dictated by the perturbativeα function for 6/g²>6.15. Speaker at the conference; on leave from CRIP, Budapest.     

三带Hubbard模型中环形电流相的量子蒙特卡罗模拟

运用约束路径量子蒙特卡罗方法,对二维、三带Hubbard模型中的环形电流相进行数值模拟。在数值模拟过程中定义了表征环流相的不同算符及其关联函数,并且选用合理的模型Hamiltonian量中的参数。通过模拟发现,对应于闭合环形的关联函数在相同距离上要比其他所有没有闭合的关联函数大得多,因此证明在三带Hubbard模型中存在环形电流相。     

Quantum dynamics at finite temperature: Time-dependent quantum Monte Carlo study

In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows a self-consistent treatment of the system of particles together with bath oscillators first for imaginary-time propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the path-integral related techniques where the real time propagation can be a challenge.     

A stochastic lattice gas for Burgers' equation: A practical study

We continue our investigation of stochastic lattice gases as a (highly parallel) means of simulating given PDEs, in this case Burgers' equation in one dimension. The lattice dynamics consists of stochastic unidirectional particle displacement, and our attention is turned toward the reliability of the model, i.e., its ability to reproduce the unique physical solution of Burgers' equation. Lattice gas results are discussed and compared against finite-difference calculations and exact solutions in examples which include shocks and rarefaction waves.     

Superconductivity and antiferromagnetism in the phase diagram of the frustrated Hubbard model within a variational study

The interplay between antiferromagnetism (AF) and superconductivity (SC) in cuprates is studied for the two-dimensional Hubbard model with a diagonal transfer t′, using a variational Monte Carlo method. Optimizing an improved function for strongly correlated values of U/t, we construct phase diagrams in the δ (doping rate)-t′/t space. It is found that the stable state is sensitive to the value of model parameters: For the extremely large values of U/t, a coexisting state is realized for t′/t ? −0.15, whose range of doping rate extends as t′/t increases. In contrast, for t′/t = −0.3, AF and SC states are mutually exclusive, and a coexisting state does not appear. As U/t decreases, the area of pure AF extends, and that of coexisting state shrinks. As a result, the coexisting state disappears for t′/t = −0.15 and U/t = 12, probable values for hole-doped cuprates. Compared with the t–J model, the Hubbard model has richer phases.     

Collapse transition and asymptotic scaling behavior of lattice animals: Low-temperature expansion

A low-temperature expansion for the free energy density of lattice animals is derived. Analysis of the series yields a collapse transition temperature ofT _c - 0.54, in close agreement with previous estimates. It is demonstrated that _p,k, the number ofp-particle,p-bond animals, obeys the asymptotic scaling law log _p,k pg(k/p) + o(p). The low-temperature series and numerical data are used to estimate the scaling function.     

The roughening transition of the three-dimensional Ising interface: A Monte Carlo study

We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite-size scaling method. The particular method has recently been proposed and successfully tested for various solid-on-solid models. The basic idea is the matching of the renormalization-groupflow of the interface with that of the exactly solvable body-centered cubic solid-on-solid model. We unambiguously confirm the Kosterlitz-Thouless nature of the roughening transition of the Ising interface. Our result for the inverse transition temperatureK _r=0.40754(5) is almost two orders of magnitude more accurate than the estimate of Mon, Landau, and Stauffer.     

Two-dimensional lattice tree exponents and amplitudes: Simulation algorithms versus series

We use a local Monte Carlo algorithm to simulate lattice trees in two dimensions for the site and bond problem. We investigate the properties of radius of gyration, perimeter-to-site ratio, and vertex degree in a tree, adding some new results in the site problem, compare our results on their noncritical properties with those obtained from earlier reversible and slightly nonreversible algorithms, and combine our determinations with new exact series expansion data. On the controversy surrounding the possible lack of universality for the first confluent singularity for the gyration radius, we feel that conclusions must be guarded.     

First-principles study of the high pressure phase transition and lattice dynamics of cerium

We present a first-principles study of the phase transition and lattice dynamics of Ce within the framework of the density functional theory using the GGA+U method. Our calculated results denote that under pressure the transition path is α-Ce (fcc)→α″-Ce (monoclinic, with two atoms per unit cell)→bct-Ce (body centered tetragonal), and the transition pressures are located at 5.36 and 14.37 GPa, respectively. The equation of state in a wide range of pressure is consistent with the experimental data. During the γ-α phase transition, the magnetic moment disappears gradually, which is mainly due to the strong interaction between the 4f and 5d electrons. By calculating the free energies from phonon dispersions including electronic contribution, the obtained γ-α transition temperature at zero pressure is 148 K. From the Blackman diagram of dimensionless elastic constant ratios, we can find that both γ- and α-Ce show negative Cauchy pressure—C₄₄>C₁₂.     

Monte Carlo study of the antiferromagnetical Ising model on a centred honeycomb lattice

We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies J_A-A and J_A-B in this lattice. Our study is focused on how the ratio of J_A-B to J_A-A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, {etc} each as a function of temperature for a given ratio of J_A-B to J_A-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio J_A-B / J_A-A. This work is helpful for studying the phase transition problem of crystals composed of compounds.     

A first order superfluid-Mott insulator transition for a Bose–Hubbard model in an emergent lattice

The combination of strong correlation and emergent lattice can be achieved when quantum gases are confined in a superradiant Fabry–Perot cavity. In addition to the discoveries of exotic phases, such as density wave ordered Mott insulator and superfluid, a surprising kink structure is found in the slope of the cavity strength as a function of the pumping strength. In this article, we show that the appearance of such a kink is a manifestation of a liquid–vapour-like transition between two superfluids with different densities. The slopes in the immediate neighborhood of the kink become divergent at the liquid–vapour critical points and display a critical scaling law with a critical exponent 1 in the quantum critical region.     

Monte Carlo study of dynamic phase transition in Ising metamagnet driven by oscillating magnetic field

The dynamical responses of Ising metamagnet (layered antiferromagnet) in the presence of a sinusoidally oscillating magnetic field are studied by Monte Carlo simulation. The time average staggered magnetisation plays the role of dynamic order parameter. A dynamical phase transition was observed and a phase diagram was plotted in the plane formed by field amplitude and temperature. The dynamical phase boundary is observed to shrink inward as the relative antiferromagnetic strength decreases. The results are compared with that obtained from pure ferromagnetic system. The shape of dynamic phase boundary observed to be qualitatively similar to that obtained from previous meanfield calculations.     

三维X-Y模型的滞后标度和动态相变行为

采用Monte Carlo方法对3DX-Y模型进行数值模拟计算，研究了在非线性外场驱动下3DX-Y模 型的滞后标度和动态相变.得出了滞后标度关系为Area～h^α₀ωβ(1-T/T_c)^γ， 其中α=0.57，β=0.34，γ=0.90.发现其动态相变行为在一定的临界参数条件下，初始短周 期(周期数PN≤10)内的结果具有与Ising模型类似的对称性破缺；但在长周期内(PN≥200)的 结果则明显区别于Ising模型而与Heisenberg模型相近，也即无稳定动态有序铁磁相的存在. 关键词： X-Y模型 滞后标度 动态相变 Monte Carlo方法     

Order parameters and boundary effects in U(1) lattice gauge theory

We show that, independently of the boundary conditions, the two phases of the 4-dimensional compact U(1) lattice gauge theory can be characterized by the presence or absence of an “infinite” current network, with an appropriate definition of “infinite” network takes values 0 or 1 in the cold and hot phase, respectively. It thus constitutes a very efficient order parameter, which allows one to determine the transition region at low computational cost. In addition, for open and fixed boundary conditions we address the question of the impact of inhomogeneities and give examples of the reappearance of an energy gap already at moderate lattice sizes.     

Quantum coherence and ground-state phase transition in a four-chain Bose–Hubbard model

We study the quantum coherence and ground-state phase transition of a four-chain Bose–Hubbard model with the long-range interaction. In a special four-chain Bose–Hubbard model,i.e., each chain only has one optical potential, four types of the ground-state phases are discovered. The effects of the disorder, the on-site interaction and the long-range interaction on the quantum coherence are studied. For the system without the long-range interaction, the quantum coherence changes from one periodic oscillation to two periodic oscillations as the onsite interaction increases. By considering the long-range interaction, the quantum coherence goes back to one periodic oscillation again. The on-site interaction itself suppresses the quantum coherence, both the on-site interaction and long-range interaction together enhance the quantum coherence with the weak disorder. If the disorder strength is increased beyond a critical value,they start to suppress the quantum coherence. In a regular four-chain Bose–Hubbard model, i.e.,each chain has many optical potentials, the ground-state phase transitions are obtained by using the cluster Gutzwiller mean-field method. Exotic ground-state phases are found, i.e., superfluid phase, integer Mott insulator phase, supersolid phase and loophole insulator phase. The combination of the loophole insulator phase and the supersolid phase expands the lobes with the half-integer filling per site for the small ratio β = t_■/t_⊥.