Symmetric non-Hermitian skin effect with emergent nonlocal correspondence

The non-Hermitian skin effect (NHSE) refers to the extensive number of eigenstates of a non-Hermitian system that are localized in open boundaries. Here, we predict a universal phenomenon that the local particle-hole(-like) symmetry (PHS) leads to nonlocal pairs of skin modes distributed on different boundaries, manifesting a 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 nonlocal 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.