# Worldline approach to few-body physics on the lattice

## TL;DR

This paper introduces a worldline approach using worm algorithms to efficiently simulate few-body non-relativistic bosons and fermions on a lattice, addressing sign problems and analyzing fermion permutation signs.

## Contribution

The paper develops a novel worldline formulation with worm algorithms for non-relativistic particles, enabling efficient sampling and sign problem analysis in lattice simulations.

## Key findings

- Efficient sampling of fixed particle-number sectors using worm algorithms.
- Application of the method to non-relativistic fermions, treating permutation signs as observables.
- Identification of limitations in complex Langevin methods for 1D fermions.

## Abstract

We study the physics of two species of non-relativistic hard-core bosons with attractive or repulsive delta function interactions on a spacetime lattice using the worldline formulation. By tuning the chemical potential carefully we show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector. Since fermions can be treated as hard-core bosons up to a permutation sign, we also apply this approach to non-relativistic fermions. The fermion permutation sign is treated as an observable in this approach and can be used to extract energies for each particle-number sector. Since in one dimension non-relativistic fermions can only permute due to boundary effects, unlike the auxiliary field method, in many cases our approach does not suffer from sign problems. Using our method we discover limitations of the recently proposed complex Langevin calculations in one dimension.