# Few-body physics on a space-time lattice in the worldline approach

## TL;DR

This paper develops a worldline lattice approach with worm algorithms for simulating few-body non-relativistic bosons and fermions, revealing advantages over traditional methods and potential ways to mitigate the fermion sign problem.

## Contribution

It introduces a novel worldline lattice method with worm algorithms for non-relativistic particles, enabling efficient sampling and fermion sign analysis, and assesses its limitations and potential in higher dimensions.

## Key findings

- Efficient sampling of worldline configurations in fixed particle-number sectors.
- Fermion permutation sign as an observable for energy extraction.
- Demonstrates the method's advantages over auxiliary field approaches in 1D.

## Abstract

We formulate the physics of two species of non-relativistic hard-core bosons with attractive or repulsive delta function interactions on a space-time lattice in the worldline approach. We show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector if the chemical potential is tuned carefully. Since fermions can be treated as hard-core bosons up to a permutation sign, we apply this approach to study non-relativistic fermions. The fermion permutation sign is an observable in this approach and can be used to extract energies in each particle-number sector. In one dimension, non-relativistic fermions can only permute across boundaries, and so our approach does not suffer from sign problems in many cases, unlike the auxiliary field method. Using our approach, we discover limitations of the recently proposed complex Langevin calculations in one spatial dimension for some parameter regimes. In higher dimensions, our method suffers from the usual fermion sign problem. Here we provide evidence that it may be possible to alleviate this problem for few-body physics