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arXiv 0704.3792cond-mat.str-elcond-mat.stat-mech
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基于高斯基的Monte Carlo方法研究游荡和强关联电子系统的基态

Gaussian-Basis Monte Carlo Method for Numerical Study on Ground States of Itinerant and Strongly Correlated Electron Systems

Takeshi Aimi, Masatoshi Imada

摘要:

本文研究了由Corney和Drummond提出的高斯基蒙特卡罗方法(GBMC)。这种方法是基于扩展的密度矩阵算子ρ的相干高斯型算子的基础λ的装置,并不遭受负号的问题。但由于样品常处于亚稳态或对称性破缺态,原方法往往不能再现真实基态,导致计算的物理量存在系统误差。为了克服这个困难,我们结合Assaad,Werner,Corboz,Gull和Troyer提出的量子数投影方案,结合原始GBMC方法的重要性采样。这种改进使我们能够在量子数投影相空间中进行重要性采样。与已有的量子数投影方法的比较表明,该方法加快了对基态的收敛速度,从而扩展了GBMC方法的适用范围和参数选择范围.本方案为强关联电子系统的计算提供了一种有效的实用方法,超出了其他计算方法如量子蒙特卡罗方法所能处理的系统尺寸、相互作用强度和晶格结构的范围。

英文摘要:

We examine Gaussian-basis Monte Carlo method (GBMC) introduced by Corney and Drummond. This method is based on an expansion of the density-matrix operator rho by means of the coherent Gaussian-type operator basis Lambda and does not suffer from the minus sign problem. The original method, however, often fails in reproducing the true ground state and causes systematic errors of calculated physical quantities because the samples are often trapped in some metastable or symmetry broken states. To overcome this difficulty, we combine the quantum-number projection scheme proposed by Assaad, Werner, Corboz, Gull and Troyer in conjunction with the importance sampling of the original GBMC method. This improvement allows us to carry out the importance sampling in the quantum-number-projected phase-space. Some comparisons with the previous quantum-number projection scheme indicate that, in our method, the convergence with the ground state is accelerated, which makes it possible to extend the applicability and widen the range of tractable parameters in the GBMC method. The present scheme offers an efficient practical way of computation for strongly correlated electron systems beyond the range of system sizes, interaction strengths and lattice structures tractable by other computational methods such as the quantum Monte Carlo method.

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