Symmetric non-Hermitian skin effect with emergent nonlocal correspondence

TL;DR

This paper predicts a universal nonlocalized skin effect in non-Hermitian systems with particle-hole symmetry, linking skin modes to topological zero modes via an extended Hermitian framework, and proposes optical lattice experiments for observation.

Contribution

It introduces a novel nonlocal symmetry-protected non-Hermitian skin effect and develops a generic theory connecting skin modes to topological zero modes through an extended Hermitian Hamiltonian.

Findings

Skin modes are distributed on different boundaries due to local PHS.

The theory maps skin modes to topological zero modes in an extended Hermitian space.

Proposed optical Raman lattice models enable experimental observation.

Abstract

The non-Hermitian skin effect (NHSE) refers to that an extensive number of eigenstates of a non-Hermitian system are localized in open boundaries. Here we predict a universal phenomenon that with local particle-hole(-like) symmetry (PHS) the skin modes must be equally distributed on different boundaries, manifesting a novel nonlocalization of the local PHS, which is unique to non-Hermitian systems. We develop a generic theory for the emergent nonlocal symmetry-protected NHSE by connecting the non-Hermitian system to an extended Hermitian Hamiltonian in a quadruplicate Hilbert space, which maps the skin modes to the topological zero modes and the PHS to an emergent nonlocal symmetry in the perspective of many body physics. The predicted NHSE is robust against perturbations. We propose optical Raman lattice models to observe the predicted phenomena in all physical dimensions, which are accessible with cold-atom experiments.