Universal SSE algorithm for Heisenberg model and Bose Hubbard model with interaction.pdf

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2017-04-09 发布于江苏
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Universal SSE algorithm for Heisenberg model and Bose Hubbard model with interaction.pdf

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Universal SSE algorithm for Heisenberg model and Bose Hubbard model with interaction

a r X i v : c o n d - m a t / 0 3 0 2 6 1 4 v 1 [ c o n d - m a t .s t a t - m e c h ] 2 8 F e b 2 0 0 3 Universal SSE algorithm for Heisenberg model and Bose Hubbard model with interaction M. V. Zyubin? and V. A. Kashurnikov? Moscow Engineering Physics Institute, 115409 Moscow, Russia (Dated: February 2, 2008) We propose universal SSE method for simulation of Heisenberg model with arbitrary spin and Bose Hubbard model with interaction. We report on the first calculations of soft-core bosons with interaction by the SSE method. Moreover we develop a simple procedure for increase efficiency of the algorithm. From calculation of integrated autocorrelation times we conclude that the method is efficient for both models and essentially eliminates the critical slowing down problem. PACS numbers: 05.10.Ln, 05.30.Jp, 75.10.Jm I. INTRODUCTION Recently, significant progress in quantum Monte Carlo methods has been observed. During the last two decades, advanced quantumMonte Carlo algorithms have been de- veloped. First quantum Monte Carlo methods, so-called world line algorithms, were based on Suzuki-Trotter ap- proximation and used local updates [1, 2]. It has been replaced by the loop algorithms, wich use non-local up- dates. Using of non-local loop updates allows to decrease autocorrelation times by orders of magnitude [3]. Later the loop algorithms in continuous imaginary time have been developed [4]. The continuous-time implementa- tion of the loop algorithm has eliminated errors result- ing from the Trotter discretization and, hence, loop al- gorithms have become numerically exact methods. Unfortunately, loop algorithms are inefficient in the presence of external field [5]. The origin of this slow- down results from the method of including external field into the simulations. External field is taken into account through the global weight, which increases with field in- crease. To construct efficient algorithm one should takes into account external field locally, i