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. 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.

13 pages, 6 figures, to appear in Annalen der Physik (Wiley)

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Cited by in corpus (7)

• Non-reciprocal dynamics and the non-Hermitian skin effect of repulsively bound pairs
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Interaction-Induced Second-Order Skin Effect
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory