Limits of the Quantum Monte Carlo method
Z. Neda, Z. Dezso
TL;DR
This paper explores the limitations of Quantum Monte Carlo methods in one-dimensional quantum systems, highlighting issues with ring geometries, fermion frustration, and the minus-sign problem for bosons.
Contribution
It identifies specific scenarios where Quantum Monte Carlo methods fail or produce unphysical results in one-dimensional quantum systems.
Findings
QMC is inapplicable for ring geometries
Unphysical frustration occurs for interacting fermions
Minus-sign problem affects interacting bosons
Abstract
We consider the one-dimensional quantum-statistical problem of interacting spin-less particles in an infinite deep potential valley and on a ring. Several limits for the applicability of the Quantum Monte Carlo (QMC) methods were revealed and discussed. We show the inapplicability of the QMC method for ring-like geometries, realize an unphysical frustration for interacting fermions and a minus-sign problem for interacting bosons.
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Taxonomy
TopicsTheoretical and Computational Physics · Advanced Chemical Physics Studies