Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model

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. Despite the complexity arising from many-body interactions, the local gauge symmetry enables the exact construction of a steady state that displays 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.

Figures (2)

• Figure 1: (a) Dissipative quantum link model with $H$ in Eq.\ref{['eq:hamiltonian']}. (b) Liouvillian spectrums and (c) steady-state density distributions $N_n=\operatorname{Tr}[\rho_{\text{ss},N}( \tau_n+1/2)]$ numerically obtained by the exact diagonalization in the sector $\mathcal{G}_n=0$ and $N=2$ with parameters $L=7$, $J=1$, $\gamma_u=2.4$, and $\gamma_d=1.6$. We consider both the periodic (gray color) and open (red color) boundary conditions. Black points in (b) mark the eigenvalues of exact OBC eigenoperators. (d) The asymmetric particle distributions obtained from the exact OBC steady state. $\nu=N/L$ is the filling factor. We take $\beta=\gamma_u/\gamma_d=3$ and $L=24$.
• Figure 2: (a) Generalized dissipative QLM. (b,c) Steady-state distribution of the middle and top layers. With $L=14$ and $\beta=3$, we show the results in the charge sector $( N_{H^\prime}, D_{H^\prime})=(0,0)$.