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arXiv:physics/0002031 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Path-integral Monte Carlo simulations without the sign problem: Multilevel blocking approach for effective actions

Reinhold Egger, Lothar Mühlbacher, Chi H. Mak

Published May 1, 2000• 72 citations
arXivHTMLPDF

Abstract

The multilevel blocking algorithm recently proposed as a possible solution to the sign problem in path-integral Monte Carlo simulations has been extended to systems with long-ranged interactions along the Trotter direction. As an application, results for the real-time quantum dynamics of the spin-boson model are presented.
DOI
10.1103/physreve.61.5961

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This article gives an introduction to the multilevel blocking (MLB) approach to both the fermion and the dynamical sign problem in path-integral Monte Carlo simulations. MLB is able to substantially relieve the sign problem in many situations. Besides an exposition of the method, its accuracy and several potential pitfalls are discussed, providing guidelines for the proper choice of certain MLB parameters. Simulation results are shown for strongly interacting electrons in a 2D parabolic quantum dot, the real-time dynamics of several simple model systems, and the dissipative two-state dynamics (spin-boson problem).
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A practical method to tackle the sign problem in real-time path integral simulations is proposed based on the multilevel blocking idea. The formulation is made possible by using a cumulant expansion of the action, which in addition to addressing the sign problem, provides an unbiased estimator for the action from a statistically noisy sample of real-time paths. The cumulant formulation also allows the analytical gradients of the action to be computed with little extra computational effort, and it can easily be implemented in a massively parallel environment.
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