Partial solvability induced by dark states in a box trap with decentered two-body interaction

TL;DR

This paper studies a one-dimensional box trap with a decentered two-body interaction, revealing that dark states lead to partial solvability by creating exactly solvable subspaces within the spectrum.

Contribution

It introduces a nonintegrable model with decentered interactions and demonstrates the existence of dark states that induce partial solvability.

Findings

Dark states are unaffected by the interaction and form exactly solvable subspaces.

The model's spectrum is structured by dark states, separating interacting and noninteracting sectors.

Conditions for the emergence of dark states are characterized.

Abstract

We consider a generalization of the two-body contact interaction for nonrelativistic particles confined to a one-dimensional box, in which the interaction is decentered, i.e., the particles interact only when they are separated by a distance c. In contrast to the harmonically trapped system, this model is nonintegrable. Despite this, we demonstrate that the system exhibits partial solvability due to the presence of dark states, i.e., bosonic or fermionic states unaffected by the interaction. These states form exactly solvable subspaces embedded within an interacting spectrum. We characterize the stationary properties of the system, identify the conditions for the appearance of dark states, and show how they structure the spectrum and delineate interacting and noninteracting sectors.