Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates

TL;DR

This paper investigates how eigenstates of chaotic Bose-Hubbard Hamiltonians evolve with coupling strength, using analytical and numerical methods, primarily focusing on the quantum trimer but applicable to larger systems.

Contribution

It introduces a methodology combining perturbative and semiclassical analysis to study eigenstate structure changes in Bose-Hubbard models as coupling varies.

Findings

Eigenstates show significant structural changes with increasing coupling.

The methodology is effective for analyzing larger lattice systems.

Analytical and numerical results agree on eigenstate evolution patterns.

Abstract

We consider a family of chaotic Bose-Hubbard Hamiltonians (BHH) parameterized by the coupling strength $k$ between neighboring sites. As $k$ increases the eigenstates undergo changes, reflected in the structure of the Local Density of States. We analyze these changes, both numerically and analytically, using perturbative and semiclassical methods. Although our focus is on the quantum trimer, the presented methodology is applicable for the analysis of longer lattices as well.