Delocalization of skin steady states

The skin effect, characterized by the tendency of particles to accumulate at the boundaries, has been extensively studied in non-Hermitian systems. In this paper, we propose an intuitive Lindbladian composed of two chains with reversed skin localization. The skin steady state is gradually delocalized as the interchain coupling increases. In the single-body scenario, it corresponds to a shift in the scaling of the Liouvillian gap $\mathrm{\ensuremath{\Delta}}$ from $\mathrm{\ensuremath{\Delta}}\ensuremath{\propto}{N}^{0}$ to $\mathrm{\ensuremath{\Delta}}\ensuremath{\propto}{N}^{\ensuremath{-}2}$. Notably, exact diagonalization results reveal a system-size sensitivity of the single-particle Liouvillian spectrum, inherited from the system-size sensitivity of the non-Hermitian effective Hamiltonian. We predict that even an arbitrarily small coupling will induce dramatic changes in the Liouvillian spectrum and steady state in the thermodynamic limit, a phenomenon we term the critical Liouvillian skin effect. Additionally, in the many-body scenario, by employing the stochastic Schr"odinger equation to unravel the Lindblad master equation, it is revealed that the scaling behavior of steady-state entanglement changes from the area law to the logarithmic law. In this paper, we demonstrate the delocalization of both single- and many-body skin steady states, introducing a mechanism for inducing entanglement transitions beyond the quantum Zeno effect.