Spectral density of interacting pairs in low-dimensional finite lattices

TL;DR

This paper computes the spectral density of bound pairs in low-dimensional finite lattices using Green's functions, revealing energy bandwidths for maximizing bound pairs across different interaction strengths.

Contribution

It introduces an efficient recursion method in real space to compute spectral densities for bound pairs in 1D, 2D, and Bethe lattices, covering weak to strong interactions.

Findings

Spectral profiles indicate energy ranges for optimal bound pair formation.

Method effectively handles different lattice geometries and interaction regimes.

Results provide insights into bound pair behavior in low-dimensional systems.

Abstract

The spectral density of bound pairs in ideal 1D, 2D and Bethe lattices is computed for weak and strong interactions. The computations are performed with Green's functions by an efficient recursion method in real space. For the range of interaction strengths within which bound states are predominantly single pairs, the spectral profiles guide to the energy bandwidths where the bound pairs can be maximized.