Resolution of the Sign Problem for a Frustrated Triplet of Spins

Abstract

We propose a mechanism for solving the `negative sign problem'---the inability to assign non-negative weights to quantum Monte Carlo configurations---for a toy model consisting of a frustrated triplet of spin-$1/2$ particles interacting antiferromagnetically. The introduced technique is based on the systematic grouping of the weights of the recently developed off-diagonal series expansion of the canonical partition function [Phys. Rev. E 96, 063309 (2017)]. We show that while the examined model is easily diagonalizable, the sign problem it encounters can nonetheless be very pronounced, and we offer a systematic mechanism to resolve it. We discuss the generalization of the suggested scheme and the steps required to extend it to more general and larger spin models.

12 pages, 5 figures

References in corpus (2)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Off-Diagonal Series Expansion for Quantum Partition Functions

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