Supersymmetric quantum mechanics on the lattice: I. Loop formulation

TL;DR

This paper introduces a loop formulation approach for simulating supersymmetric quantum mechanics on the lattice, effectively addressing the fermion sign problem in low-dimensional models, and provides detailed reformulations for various discretizations.

Contribution

It presents a novel fermion loop-based lattice formulation for supersymmetric quantum mechanics, solving the fermion sign problem in low dimensions and enabling more accurate simulations.

Findings

Loop formulation simplifies supersymmetric quantum mechanics simulations.

The approach effectively resolves the fermion sign problem in low dimensions.

Detailed reformulations for multiple lattice discretizations are provided.

Abstract

Simulations of supersymmetric field theories 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. For N = 2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper - the first in a series of three - we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.