Spectral Structure and Doublon Dissociation in the Two‐Particle Non‐Hermitian Hubbard Model

Abstract

Strongly‐correlated systems in non‐Hermitian models are an emergent area of research. Herein, a non‐Hermitian Hubbard model is considered, 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, a spectral phase transition of the Mott‐Hubbard band on the infinite lattice is predicted 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.