Green's functions on finite lattices and their connection to the infinite lattice limit

TL;DR

This paper demonstrates how to derive Green's functions on finite lattices from those on infinite lattices using translation operators, with explicit examples in one and two dimensions.

Contribution

It introduces a method to obtain finite lattice Green's functions from infinite lattice solutions using translation operators, providing explicit examples.

Findings

Finite lattice Green's functions can be derived from infinite lattice functions.

Explicit solutions are provided for 1D and 2D lattices.

The method simplifies calculations of Green's functions on finite lattices.

Abstract

It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.