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Journal Article

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


Sentef,  M. A.
Theoretical Description of Pump-Probe Spectroscopies in Solids, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Zhang, S.-B., Denner, M. M., Bzdušek, T., Sentef, M. A., & Neupert, T. (2022). Symmetry breaking and spectral structure of the interacting Hatano-Nelson model. Physical Review B, 106(12): L121102. doi:10.1103/PhysRevB.106.L121102.

Cite as: https://hdl.handle.net/21.11116/0000-0009-E8BA-0
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. Our results contribute to an understanding of fermionic many-body systems with non-Hermitian Hamiltonians.