The directed-loop algorithm

Details The directed-loop algorithm The directed-loop algorithm

2003-06-21

arxiv.org/abs/cond-mat/0306542v1

Physics

Condensed Matter

Strongly Correlated Electrons

10 pages, for the proceedings of "The Monte Carlo Method in the Physical Sciences: Celebrating the 50th Anniversary of the Met

Scientific paper

10.1063/1.1632141

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.

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