Fate of Two-Particle Bound States in the Continuum in non-Hermitian Systems

TL;DR

This paper investigates two-particle bound states in the continuum within non-Hermitian, nonreciprocal lattice systems, revealing how non-reciprocal hopping influences their localization and phase diagrams.

Contribution

It provides an exact Bethe-ansatz solution for BICs in non-Hermitian systems and identifies two types of BICs with analytical threshold conditions.

Findings

Non-reciprocal hopping can delocalize BICs.

Two types of BICs with different spatial distributions are identified.

Analytical thresholds for BIC breakdown are derived.

Abstract

We unveil the existence of two-particle bound state in the continuum (BIC) in a one-dimensional interacting nonreciprocal lattice with a generalized boundary condition. By applying the Bethe-ansatz method, we can exactly solve the wavefunction and eigenvalue of the bound state in the continuum band, which enable us to precisely determine the phase diagrams of BIC. Our results demonstrate that the non-reciprocal hopping can delocalize the bound state and thus shrink the region of BIC. By analyzing the wavefunction, we identify the existence of two types of BICs with different spatial distributions and analytically derive the corresponding threshold values for the breakdown of BICs. The BIC with similar properties is also found to exist in another system with an impurity potential.