Spectral analysis of two-dimensional Bose-Hubbard models

TL;DR

This paper investigates the spectral properties of two-dimensional Bose-Hubbard models, revealing a transition from regular to chaotic spectral statistics influenced by lattice connectivity and boundary conditions.

Contribution

It extends the analysis of spectral transitions from 1D to 2D Bose-Hubbard models, exploring how lattice connectivity affects spectral regularity and chaos.

Findings

Transition from regular to chaotic spectral statistics in 2D models

Higher connectivity leads to more regular spectral behavior

Mean-field approaches are valid for systems with maximal connectivity

Abstract

One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest-neighbor couplings at each site.