Numerical Studies on Correlations in Dynamics and Localization of Two Interacting Particles in Lattices

TL;DR

This paper investigates how interactions affect the dynamics and localization of two particles in lattice systems, using numerical methods to analyze 1D and 2D models including disordered and ideal lattices.

Contribution

It introduces a recursion-based numerical algorithm for two-particle Green's functions in 2D systems, enabling detailed spectral and localization analysis.

Findings

Differences in dynamics between attractive and repulsive interactions in 1D lattices.

Accurate spectral properties of 2D Hubbard and Hofstadter models computed.

Localization parameters of 2D disordered systems determined.

Abstract

Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping, differences between dynamics of attractively and repulsively interacting particles are noted. For calculations of 2D systems, a recursion based numerical algorithm for two-particle Greens functions is implemented which provides accurate results. Using this algorithm, spectral properties of 2D Hubbard and Hofstadter models is computed, along with localization parameters of 2D disordered systems.