Fermion-dimer scattering using an impurity lattice Monte Carlo approach and the adiabatic projection method

TL;DR

This paper introduces a new impurity lattice Monte Carlo method combined with the adiabatic projection technique to accurately compute fermion-dimer scattering phase shifts on the lattice, validated against exact and continuum results.

Contribution

The paper develops and applies a novel impurity lattice Monte Carlo algorithm alongside the adiabatic projection method for precise fermion-dimer scattering calculations.

Findings

Accurate phase shifts obtained for s-wave, p-wave, and d-wave channels.

Good agreement with exact lattice and continuum solutions.

Demonstration of the method's effectiveness for low-energy scattering studies.

Abstract

We present lattice Monte Carlo calculations of fermion-dimer scattering in the limit of zero-range interactions using the adiabatic projection method. The adiabatic projection method uses a set of initial cluster states and Euclidean time projection to give a systematically improvable description of the low-lying scattering cluster states in a finite volume. We use L\"uscher's finite-volume relations to determine the s-wave, p-wave, and d-wave phase shifts. For comparison, we also compute exact lattice results using Lanczos iteration and continuum results using the Skorniakov-Ter-Martirosian equation. For our Monte Carlo calculations we use a new lattice algorithm called impurity lattice Monte Carlo. This algorithm can be viewed as a hybrid technique which incorporates elements of both worldline and auxiliary-field Monte Carlo simulations.