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arXiv:cond-mat/0312675 · Journal of the Physical Society of Japan

Recent Developments of World-Line Monte Carlo Methods

Naoki Kawashima, Kenji Harada

Published Jun 15, 2004• 126 citations
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Abstract

World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -- the loop algorithm, the worm algorithm, and the directed-loop algorithm -- for updating world-line configurations are presented in a unified perspective. Detailed descriptions of the algorithms in specific cases are also given.

DOI
10.1143/jpsj.73.1379

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World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -- the loop algorithm, the worm algorithm, and the directed-loop algorithm -- for updating world-line configurations are presented in a unified perspective. Detailed descriptions of the algorithms in specific cases are also given.
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The directed‐loop scheme is a framework for generalized loop‐type updates in quantum Monte Carlo, applicable both to world‐line and stochastic series expansion methods. Here, the directed‐loop equations, the solution of which gives the probabilities of the various loop‐building steps, are discussed in the context of the anisotropic S = 1/2 Heisenberg model in a uniform magnetic field. This example shows how the directed‐loop concept emerges as a natural generalization of the conventional loop algorithm, where the loops are selfavoiding, to cases where selfintersection must be allowed in order to satisfy detailed balance.