Effective Range Expansion for the Interaction Defined on the Lattice

TL;DR

This paper presents a method to relate lattice interaction parameters to the two-body T matrix, accounting for finite lattice spacing effects, and derives their connection to effective range expansion parameters for large lattices.

Contribution

It introduces a computational scheme linking lattice interaction parameters to the two-body T matrix, including finite lattice spacing effects, and derives their relation to effective range expansion parameters.

Findings

Derived the relation between lattice interaction parameters and the T matrix.

Developed a computational scheme incorporating finite lattice spacing effects.

Established the connection to effective range expansion parameters for large lattices.

Abstract

The relation between the interaction parameters for fermions on the spatial lattice and the two-body $T$ matrix is discussed. The presented method allows determination of the interaction parameters through the relatively simple computational scheme which include the effect of finite lattice spacing. In particular the relation between the interaction parameters and the effective range expansion parameters is derived in the limit of large lattices.