Pair functions computed recursively in ordered and disordered lattices

TL;DR

This paper investigates the pairing of two interacting particles in various lattice structures using a recursive method that avoids integrations, with potential for larger disordered systems through approximations.

Contribution

It applies a recursive approach to compute pair functions in ideal lattices, extending the method's applicability to disordered systems.

Findings

Recursive method effectively computes pair functions in 1D, 2D, and Bethe lattices.

Disordered systems can be analyzed with larger sizes using approximations.

Method avoids complex integrations, simplifying calculations.

Abstract

In this article I study pairing of two interacting particles in ideal 1D, 2D and Bethe lattices. I employ the method of recursion that has been formulated recently by Berciu et. al. to compute the pair functions in real space without performing any integrations. Although, in higher dimensions the system sizes that can be addressed with this method become limited, for disordered systems this size limit can be increased by employing approximations.