Simulation of supersymmetric models on the lattice without a sign problem

TL;DR

This paper introduces a novel lattice simulation method for supersymmetric models that avoids the fermion sign problem by using fermion loops, enabling accurate computation of the Witten index and spectrum.

Contribution

The authors develop a fermion loop formulation and a specialized simulation algorithm to solve the sign problem in low-dimensional supersymmetric lattice models.

Findings

Successful simulation of N=2 supersymmetric quantum mechanics

Accurate calculation of the Witten index and spectrum

Demonstration of the method's effectiveness in low dimensions

Abstract

Simulations of supersymmetric models on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. The formulation is based on the exact hopping expansion of the fermionic action and allows the explicit decomposition of the partition function into bosonic and fermionic contributions. We devise a simulation algorithm which separately samples the fermionic and bosonic sectors, as well as the relative probabilities between them. The latter then allows a direct calculation of the Witten index and the corresponding Goldstino mode. Finally, we present results from simulations on the lattice for the spectrum and the Witten index for N=2 supersymmetric quantum mechanics.