Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms

TL;DR

This paper introduces an efficient simulation algorithm for supersymmetric quantum mechanics on the lattice that overcomes the fermion sign problem and remains effective in the massless limit, enabling better exploration of supersymmetry breaking.

Contribution

It presents a novel fermion simulation algorithm based on topological sector separation that solves the fermion sign problem and avoids critical slowing down in supersymmetric lattice models.

Findings

Algorithm guarantees tunnelling between topological sectors.

No critical slowing down in the massless limit.

Efficient handling of Goldstino mode in broken supersymmetry.

Abstract

In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a fluctuating open fermion string. It guarantees sufficient tunnelling between the topological sectors, and hence provides a solution to the fermion sign problem affecting systems with broken supersymmetry. Moreover, the algorithm shows no critical slowing down even in the massless limit and can hence handle the massless Goldstino mode emerging in the supersymmetry broken phase. In this paper -- the third in a series of three -- we present the details of the simulation algorithm and demonstrate its efficiency by means of a few examples.