Collective non-Hermitian skin effect: point-gap topology and the doublon-holon excitations in non-reciprocal many-body systems

Open quantum systems provide a plethora of exotic topological phases of matter that have no Hermitian counterpart. Non-Hermitian skin effect, macroscopic collapse of bulk states to the boundary, has been extensively studied in various experimental platforms. However, it remains an open question whether such topological phases persist in the presence of many-body interactions. Previous studies have shown that the Pauli exclusion principle suppresses the skin effect. In this study, we present a counterexample by demonstrating the presence of the skin effect in doublon-holon excitations. While the ground state of the spin-half Hatano-Nelson model shows no skin effect, the doublon-holon pairs, as its collective excitations, display the many-body skin effect even in strong coupling limit. We establish the robustness of this effect by revealing a bulk-boundary correspondence mediated by the point gap topology within the many-body energy spectrum. Our findings underscore the existence of non-Hermitian topological phases in collective excitations of many-body interacting systems. In this paper the authors explain the many-body non-Hermitian skin effect (NHSE) from the angle of doublon-holon pairs in the spin-full Hatano-Nelson model. The main result is that while strong interactions suppress doublon-holon pairs in the ground state, leading to the absence of the NHSE, excited eigenstates exhibit these excitations, with doublons and holons moving toward opposite directions.