Solution to the sign problem in a frustrated quantum impurity model

TL;DR

This paper presents a method to eliminate the sign problem in a frustrated quantum impurity model by mapping it to a fermionic model and pairing fermion worldlines, enabling sign-problem-free simulations.

Contribution

The authors introduce a novel approach that maps a frustrated quantum impurity model to a fermionic system and pairs worldlines to solve its sign problem.

Findings

Sign problem is eliminated through fermion worldline pairing.

Mapping to a Hubbard model facilitates the solution.

The method enables sign-problem-free simulations of the model.

Abstract

In this work we solve the sign problem of a frustrated quantum impurity model consisting of three quantum spin-half chains interacting through an anti-ferromagnetic Heisenberg interaction at one end. We first map the model into a repulsive Hubbard model of spin-half fermions hopping on three independent one dimensional chains that interact through a triangular hopping at one end. We then convert the fermion model into an inhomogeneous one dimensional model and express the partition function as a weighted sum over fermion worldline configurations. By imposing a pairing of fermion worldlines in half the space we show that all negative weight configurations can be eliminated. This pairing naturally leads to the original frustrated quantum spin model at half filling and thus solves its sign problem.