Two particles on a chain with disordered interaction: Localization and dissociation of bound states and mapping to chaotic billiards

TL;DR

This paper investigates how two interacting particles on a disordered chain exhibit localization, dissociation, and chaotic behavior, revealing new insights into bound state dynamics and quantum chaos in disordered systems.

Contribution

It introduces a detailed analysis of molecular and atomic state localization, dissociation, and chaos in a disordered two-particle chain, highlighting novel separatrix states.

Findings

Molecular bound states become Anderson localized under weak disorder.

Strong disorder causes delocalization and dissociation of the molecular band.

Atomic band exhibits signatures of quantum chaos and contains unique separatrix states.

Abstract

We consider two particles hopping on a chain with a contact interaction between them. At strong interaction, there is a molecular bound state separated by a direct gap from a continuous band of atomic states. Introducing weak disorder in the interaction, the molecular state becomes Anderson localized. At stronger disorder, part of the molecular band delocalizes and dissociates due to its hybridization to the atomic band. We characterize these different regimes by computing the density of states, the inverse participation ratio, the level-spacing statistics and the survival probability of an initially localized state. The atomic band is best described as that of a rough billiard for a single particle on a square lattice that shows signatures of quantum chaos. In addition to typical "chaotic states", we find states that are localized along only one direction. These "separatrix states" are more localized than chaotic states, and similar in this respect to scarred states, but their existence is due to the separatrix iso-energy line in the interaction-free dispersion relation, rather than to unstable periodic orbits.