Many-body approach to non-Hermitian physics in fermionic systems

TL;DR

This paper introduces a non-Hermitian many-body polarization as a topological invariant in 1D fermionic systems, establishing bulk-boundary correspondence under periodic boundary conditions and revealing symmetry-protected topological phases.

Contribution

It proposes a new topological invariant for non-Hermitian systems that satisfies bulk-boundary correspondence in PBC, addressing previous issues with boundary sensitivity.

Findings

Non-Hermitian skin effect is absent due to Pauli exclusion.

The topological invariant is quantized under certain symmetries.

Bulk-boundary correspondence is demonstrated in the non-Hermitian SSH model.

Abstract

In previous studies, the topological invariants of 1D non-Hermitian systems have been defined in open boundary condition (OBC) to satisfy the bulk-boundary correspondence. The extreme sensitivity of bulk energy spectra to boundary conditions has been attributed to the breakdown of the conventional bulk-boundary correspondence based on the topological invariants defined under periodic boundary condition (PBC). Here we propose non-Hermitian many-body polarization as a topological invariant for 1D non-Hermitian systems defined in PBC, which satisfies the bulk-boundary correspondence. Employing many-body methodology in the non-Hermitian Su-Schrieffer-Heeger model for fermions, we show the absence of non-Hermitian skin effect due to the Pauli exclusion principle and demonstrate the bulk-boundary correspondence using the invariant defined under PBC. Moreover, we show that the bulk topological invariant is quantized in the presence of chiral or generalized inversion symmetry. Our study suggests the existence of generalized crystalline symmetries in non-Hermitian systems, which give quantized topological invariants that capture the symmetry-protected topology of non-Hermitian systems.