Many-body non-Hermitian skin effect with exact steady states in dissipative lattice gauge theory

Abstract: We introduce a dissipative lattice gauge model that exhibits the many-body version of the non-Hermitian skin effect. The dissipative couplings between dynamical gauge fields on the lattice links and the surrounding environment generate chiral motions of particles residing on lattice sites. Although the system involves many-body interactions, the local gauge symmetries offer a flexible approach to exactly constructing the steady state that demonstrates the many-body non-Hermitian skin effect. Furthermore, our approach can be generalized to realize a new type of many-body non-Hermitian skin effect, dubbed the hierarchical skin effect, where different subsystem degrees of freedom exhibit boundary accumulation of multiple moments at different orders. Our findings can be readily observed by engineering dissipation in state-of-the-art lattice gauge simulators.