Symmetry breaking and spectral structure of the interacting Hatano-Nelson model

We study the Hatano-Nelson model, i.e., a one-dimensional non-Hermitian chain of spinless fermions with nearest-neighbor nonreciprocal hopping, in the presence of repulsive nearest-neighbor interactions. At half filling, we find two PT transitions, as the interaction strength increases. The first transition is marked by an exceptional point between the first and the second excited state in a finite-size system and is a first-order symmetry-breaking transition into a charge-density wave regime. Persistent currents characteristic of the Hatano-Nelson model abruptly vanish at the transition. The second transition happens at a critical interaction strength that scales with the system size and can thus only be observed in finite-size systems. It is characterized by a collapse of all energy eigenvalues onto the real axis. We further show that in a strong interaction regime, but away from half filling, the many-body spectrum shows point gaps with nontrivial winding numbers, akin to the topological properties of the single-particle spectrum of the Hatano-Nelson chain, which indicates the skin effect of extensive many-body eigenstates under open boundary conditions. Our results can be applied to other models such as the non-Hermitian Su-Schrieffer-Heeger-type model and contribute to an understanding of fermionic many-body systems with non-Hermitian Hamiltonians.

Automated summary

The Hatano-Nelson model, a one-dimensional non-Hermitian chain of spinless fermions, was studied in the presence of repulsive nearest-neighbor interactions. Two PT transitions were found, with the first one being a first-order symmetry-breaking transition into a charge-density wave regime. Persistent currents characteristic of the model disappear abruptly at this transition. The second transition, which only occurs in finite-size systems, is characterized by the collapse of all energy eigenvalues onto the real axis. In addition, in a strong interaction regime, the many-body spectrum exhibits point gaps with nontrivial winding numbers, similar to the topological properties of the single-particle spectrum of the Hatano-Nelson chain, indicating the skin effect of extensive many-body eigenstates under open boundary conditions.