Precise determination of lattice phase shifts and mixing angles

TL;DR

This paper presents a versatile and precise method for calculating lattice phase shifts and mixing angles applicable to various lattice geometries, improving accuracy over existing techniques.

Contribution

It introduces a novel approach combining angular momentum projection, spherical walls, and auxiliary potentials for accurate phase shift determination on arbitrary lattices.

Findings

Achieved high-precision phase shifts and mixing angles for coupled partial waves.

Validated method against systems with strong tensor interactions.

Applicable to diverse lattice simulation and experimental contexts.

Abstract

We introduce a general and accurate method for determining lattice phase shifts and mixing angles, which is applicable to arbitrary, non-cubic lattices. Our method combines angular momentum projection, spherical wall boundaries and an adjustable auxiliary potential. This allows us to construct radial lattice wave functions and to determine phase shifts at arbitrary energies. For coupled partial waves, we use a complex-valued auxiliary potential that breaks time-reversal invariance. We benchmark our method using a system of two spin-1/2 particles interacting through a finite-range potential with a strong tensor component. We are able to extract phase shifts and mixing angles for all angular momenta and energies, with precision greater than that of extant methods. We discuss a wide range of applications from nuclear lattice simulations to optical lattice experiments.