Spectral structure and doublon dissociation in the two-particle non-Hermitian Hubbard model

TL;DR

This paper analyzes the spectral and dynamical properties of a non-Hermitian Hubbard model with non-reciprocal hopping, revealing a phase transition, doublon dissociation in the bulk, and a boundary revival of bound states, highlighting unique non-Hermitian effects.

Contribution

It provides the first exact analytical results on the spectral structure and dynamical behavior of two-particle states in a non-Hermitian Hubbard model with non-reciprocal hopping.

Findings

Spectral phase transition from open to closed loop in complex energy plane.

Dissociation of doublons in the bulk due to non-Hermitian dynamics.

Revival of doublon states at the lattice edges, a boundary effect.

Abstract

Strongly-correlated systems in non-Hermitian models are an emergent area of research. Here we consider a non-Hermitian Hubbard model, where the single-particle hopping amplitudes on the lattice are not reciprocal, and provide exact analytical results of the spectral structure in the two-particle sector of Hilbert space under different boundary conditions. The analysis unveils some interesting spectral and dynamical effects of purely non-Hermitian nature and that deviate from the usual scenario found in the single-particle regime. Specifically, we predict a spectral phase transition of the Mott-Hubbard band on the infinite lattice as the interaction energy is increased above a critical value, from an open to a closed loop in complex energy plane, and the dynamical dissociation of doublons, i.e. instability of two-particle bound states, in the bulk of the lattice, with a sudden revival of the doublon state when the two particles reach the lattice edge. Particle dissociation observed in the bulk of the lattice is a clear manifestation of non-Hermitian dynamics arising from the different lifetimes of single-particle and two-particle states, whereas the sudden revival of the doublon state at the boundaries is a striking burst edge dynamical effect peculiar to non-Hermitian systems with boundary-dependent energy spectra, here predicted for the first time for correlated particles.