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Strongly-correlated systems in non-Hermitian models are an emergent area ofresearch. Here we consider a non-Hermitian Hubbard model, where thesingle-particle hopping amplitudes on the lattice are not reciprocal, andprovide exact analytical results of the spectral structure in the two-particlesector of Hilbert space under different boundary conditions. The analysisunveils some interesting spectral and dynamical effects of purely non-Hermitiannature and that deviate from the usual scenario found in the single-particleregime. Specifically, we predict a spectral phase transition of theMott-Hubbard band on the infinite lattice as the interaction energy isincreased above a critical value, from an open to a closed loop in complexenergy plane, and the dynamical dissociation of doublons, i.e. instability oftwo-particle bound states, in the bulk of the lattice, with a sudden revival ofthe doublon state when the two particles reach the lattice edge. Particledissociation observed in the bulk of the lattice is a clear manifestation ofnon-Hermitian dynamics arising from the different lifetimes of single-particleand two-particle states, whereas the sudden revival of the doublon state at theboundaries is a striking burst edge dynamical effect peculiar to non-Hermitiansystems with boundary-dependent energy spectra, here predicted for the firsttime for correlated particles.

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