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)PREHBM2470-004510.1103/PhysRevE.96.063309]. We show that, although 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 prospects of generalizing the suggested scheme and the steps required to extend it to more general and larger spin models.