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

• URL: http://arxiv.org/abs/2308.04505v1
• Date: Tue, 8 Aug 2023 18:12:15 GMT
• Title: Spectral structure and doublon dissociation in the two-particle non-Hermitian Hubbard model
• Authors: Stefano Longhi
• Abstract summary: We consider a non-Hermitian Hubbard model, where the single-particle hopping amplitudes on the lattice are not reciprocal. The analysis unveils some interesting spectral and dynamical effects of purely non-Hermitian nature.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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