Monte Carlo evaluation of non-Abelian statistics

We develop a general framework to (numerically) study adiabatic braiding of quasiholes in fractional quantum Hall systems. Specifically, we investigate the Moore-Read (MR) state at nu=1/2 filling factor, a known candidate for non-Abelian statistics, which appears to actually occur in nature. The non-Abelian statistics of MR quasiholes is demonstrated explicitly for the first time, confirming the results predicted by conformal field theories.     

Bose condensation of two-dimensional dipolar excitons: Simulation by the quantum Monte Carlo method

The Bose condensation of two-dimensional dipolar excitons in quantum wells is numerically studied by the diffusion Monte Carlo simulation method. The correlation, microscopic, thermodynamic, and spectral characteristics are calculated. It is shown that, in structures of coupled quantum wells, in which low-temperature features of exciton luminescence have presently been observed, dipolar excitons form a strongly correlated system.     

Monte Carlo method and sensitivity estimations

It is shown that, starting from any existing Monte Carlo algorithm for estimation of a physical quantity A, it is possible to implement a simple additional procedure that simultaneously estimates the sensitivity of A to any problem parameter. The corresponding supplementary cost is very low as no additional random sampling is required. The principle is presented on a formal basis and simple radiative transfer examples are used for illustration.     

Hierarchical Monte Carlo methods for fractal random fields

Two hierarchical Monte Carlo methods for the generation of self-similar fractal random fields are compared and contrasted. The first technique, successive random addition (SRA), is currently popular in the physics community. Despite the intuitive appeal of SRA, rigorous mathematical reasoning reveals that SRA cannot be consistent with any stationary power-law Gaussian random field for any Hurst exponent; furthermore, there is an inherent ratio of largest to smallest putative scaling constant necessarily exceeding a factor of 2 for a wide range of Hurst exponentsH, with 0.30<H<0.85. Thus, SRA is inconsistent with a stationary power-law fractal random field and would not be useful for problems that do not utilize additional spatial averaging of the velocity field. The second hierarchical method for fractal random fields has recently been introduced by two of the authors and relies on a suitable explicit multiwavelet expansion (MWE) with high-moment cancellation. This method is described briefly, including a demonstration that, unlike SRA, MWE is consistent with a stationary power-law random field over many decades of scaling and has low variance.     

Monte Carlo simulations of the classical two-dimensional discrete frustrated model

The classical two-dimensional discrete frustrated φ ⁴ model is studied by Monte Carlo simulations. The correlation function is obtained for two values of a parameter d that determines the frustration in the model. The ground state is a ferro-phase for d = - 0.35 and a commensurate phase with period N = 6 for d = - 0.45. Mean field predicts that at higher temperature the system enters a para-phase via an incommensurate state, in both cases. Monte Carlo data for d = - 0.45 show two phase transitions with a floating-incommensurate phase between them. The phase transition at higher temperature is of the Kosterlitz-Thouless type. Analysis of the data for d = - 0.35 shows only a single phase transition between the floating-fluid phase and the ferro-phase within the numerical error. Received 16 December 2002 / Received in final form 17 January 2003 Published online 6 March 2003 RID="a" ID="a"e-mail: vladimir@shg.ru     

A Monte Carlo study of the classical two-dimensional one-component plasma

We present results from extensive Monte Carlo simulations of the fluid phase of the two-dimensional classical one-component plasma (OCP). The difficulties associated with the infinite range of the logarithmic Coulomb interaction are eliminated by confining the particles to the surface of a sphere. The results are compared to those obtained for a planar system with screened Coulomb interactions and periodic boundary conditions; in this case the infinite tail of the Coulomb interaction is treated as a perturbation. The exact simulation results are used to test various approximate theories, including a semiempirical modification of the hypernetted-chain (HNC) integral equation. The OCP freezing transition is located at a coupling= e²/k_BT–140.     

Improved Monte Carlo renormalization group method

An extensive program to analyze critical systems using an improved Monte Carlo renormalization group method (IMCRG),⁽¹⁾ being undertaken at LANL and Cornell, is described. Here we first briefly rview the method and then list some of the topics being investigated.     

Application of the projector Monte Carlo method to the transfer matrix of the classical XY model

An application of the projector Monte Carlo method to the transfer-matrix eigenvalue problem is described, for the classical planar spin model. The free energy of the system is computed by the growth estimate. Importance sampling is implemented, using a mean-field approximation of the eigenfunction as a trial wave function. The mixed expectation values of spin correlations are measured by their averages in the Monte Carlo ensemble.     

Effective model for rare-earth Kitaev materials and its classical Monte Carlo simulation

Recently, the family of rare-earth chalcohalides were proposed as candidate compounds to realize the Kitaev spin liquid (KSL) [Chin. Phys. Lett. 38 047502 (2021)]. In the present work, we firstly propose an effective spin Hamiltonian consistent with the symmetry group of the crystal structure. Then we apply classical Monte Carlo simulations to preliminarily study the model and establish a phase diagram. When approaching to the low temperature limit, several magnetic long range orders are observed, including the stripe, the zigzag, the antiferromagnetic (AFM), the ferromagnetic (FM), the incommensurate spiral (IS), the multi-Q, and the 120° ones. We further calculate the thermodynamic properties of the system, such as the temperature dependence of the magnetic susceptibility and the heat capacity. The ordering transition temperatures reflected in the two quantities agree with each other. For most interaction regions, the system is magnetically more susceptible in the ab-plane than in the c-direction. The stripe phase is special, where the susceptibility is fairly isotropic in the whole temperature region. These features provide useful information to understand the magnetic properties of related materials.     

Monte Carlo simulation of the two-dimensional Potts model using nonextensive statistics

The standard Potts model is investigated in the framework of nonextensive statistical mechanics. We performed Monte Carlo simulations on two-dimensional lattices with linear sizes ranging from 16 to 64 using the Metropolis algorithm, where the classical Boltzmann–Gibbs transition probabilities were modified for the nonextensive case. We found that the Potts model undergoes a phase transition in the nonextensive scenario. We established the order of the phase transition and we computed the critical temperature for different values of the Tsallis entropic index.     

Monte Carlo simulation of ion-induced kinetic electron emission statistics from solids

Abstract

Electron emission statistics (ES) of proton-induced electron emission from Au at keV energy are investigated by applying a Monte Carlo model to describe the transport of electrons. Apparent deviations of ES from Poisson distributions are found in the same manner as experimental ES: larger probabilities for no electron emission and for emission of 2 or more electrons. At low energy, electron cascades produce an important deviation from the Poisson distribution, in addition with deviations due to the backscattering of incident ions.     

Exact quantum Monte Carlo process for the statistics of discrete systems

We propose an exact Monte Carlo approach for the statistics of discrete quantum systems that does not employ the standard partition of the imaginary time into a mesh and does not contain small parameters. The method operates with discrete objects — kinks, describing virtual transitions at different moments in time. The global statistics of the kinks is reproduced by exact local procedures, the main one being based on the known solution for an asymmetric two-level system. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 12, 853–858 (25 December 1996)     

Coherent multiple scattering effects and Monte Carlo method

Based on the comparison of the iteration procedure of solving the Bethe-Salpeter equation and the Monte Carlo method, we developed a method for simulating coherent multiple-scattering effects within the framework of a unified stochastic approach. The time correlation function and the interference component were calculated for the coherent backscattering from a multiply scattering medium.     

Diffusion Monte Carlo method with lattice regularization

We introduce an efficient lattice regularization scheme for quantum Monte Carlo calculations of realistic electronic systems. The kinetic term is discretized by a finite difference Laplacian with two mesh sizes, a and a', chosen so that the electrons can diffuse in a configuration space which is in practice indistinguishable from the continuum, and the different length scales in the system can be efficiently taken in account. The regularized Hamiltonian goes to the continuous limit for a --> 0 and allows the inclusion of nonlocal potentials in a consistent variational scheme, substantially improving the accuracy upon previous nonvariational approaches.     

A path integral centroid molecular dynamics method for Bose and Fermi statistics

We propose a path integral centroid molecular dynamics (CMD) method extended to Bose and Fermi statistics. An extended method of path integral molecular dynamics (PIMD) for such statistics is also developed as a technique of calculations of static properties. Bose PIMD and CMD simulations have been performed for bulk liquid ⁴He and ideal Bose gas, respectively. The remnant of λ transition is observed for bulk liquid ⁴He, while the effect of Bose statistics on the centroid dynamics spanning several nanoseconds is observed for ideal Bose gas.     

A Monte Carlo study of two-dimensional classical easy-plane Heisenberg models with symmetry-breaking

Monte Carlo studies of thermodynamic functions for quasi-2-dimensional classical ferromagnets are reported. Easy-plane Heisenberg models with Ising and 6-fold symmetry breaking fields in the easy-plane are emphasized as models of Rb₂CrCl₄ and CoCl₂-intercalated graphite.