Transition matrix Monte Carlo method for quantum systems

We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole range of temperature. The method is based on several recent findings in Monte Carlo techniques, such as the loop algorithm and the transition matrix Monte Carlo method. In particular, we derive an exact relation between the DOS and the expectation value of the transition probability for quantum systems, which turns out to be useful in reducing the statistical errors in various estimates.Comment: 6 pages, 4 figure

Error in Monte Carlo, quasi-error in Quasi-Monte Carlo

While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account for the error improvement advertised by the Quasi-Monte Carlo method. We advocate the construction of an estimator of stochastic nature, based on the ensemble of pointsets with a particular discrepancy value. We investigate the consequences of this choice and give some first empirical results on the suggested estimators.Comment: 41 pages, 19 figure

Estimating expected first passage times using multilevel Monte Carlo algorithm

In this paper we devise a method of numerically estimating the expected first passage times of stochastic processes. We use Monte Carlo path simulations with Milstein discretisation scheme to approximate the solutions of scalar stochastic differential equations. To further reduce the variance of the estimated expected stopping time and improve computational efficiency, we use the multi-level Monte Carlo algorithm, recently developed by Giles (2008a), and other variance-reduction techniques. Our numerical results show significant improvements over conventional Monte Carlo techniques

Combination of improved multibondic method and the Wang-Landau method

We propose a method for Monte Carlo simulation of statistical physical models with discretized energy. The method is based on several ideas including the cluster algorithm, the multicanonical Monte Carlo method and its acceleration proposed recently by Wang and Landau. As in the multibondic ensemble method proposed by Janke and Kappler, the present algorithm performs a random walk in the space of the bond population to yield the state density as a function of the bond number. A test on the Ising model shows that the number of Monte Carlo sweeps required of the present method for obtaining the density of state with a given accuracy is proportional to the system size, whereas it is proportional to the system size squared for other conventional methods. In addition, the new method shows a better performance than the original Wang-Landau method in measurement of physical quantities.Comment: 12 pages, 3 figure

Quantum Monte Carlo Study on Magnetization Processes

A quantum Monte Carlo method combining update of the loop algorithm with the global flip of the world line is proposed as an efficient method to study the magnetization process in an external field, which has been difficult because of inefficiency of the update of the total magnetization. The method is demonstrated in the one dimensional antiferromagnetic Heisenberg model and the trimer model. We attempted various other Monte Carlo algorithms to study systems in the external field and compared their efficiency.Comment: 5 pages, 9 figures; added references for section 1, corrected typo