The Liouvillian skin effect and the non-Hermitian skin effect have both been used to explain the localization of eigenmodes near system boundaries, though the former is arguably more accurate in some regimes due to its incorporation of quantum jumps. However, these frameworks predominantly focus on weak Markovian interactions, neglecting the potentially crucial role of memory effects. To address this, we investigate, utilizing the powerful hierarchical equations of motion method, how a non-Markovian environment can modify the Liouvillian skin effect. We demonstrate that a non-Markovian environment can induce a “thick skin effect,” where the skin mode broadens and shifts into the bulk. We further identify that the skin-mode quantum coherence can only be generated when the coupling contains counter-rotating terms, leading to the coherence delocalization and oscillatory relaxation with a characteristic linear scaling with system size. Remarkably, both the skin-mode and steady-state coherence exhibit resistance to decoherence from additional environmental noise. These findings highlight the profound impact of system-bath correlations on relaxation and localization, revealing unique phenomena beyond conventional Markovian approximations.
The Liouvillian skin effect and the non-Hermitian skin effect have both been used to explain the localization of eigenmodes near system boundaries, though the former is arguably more accurate in some regimes due to its incorporation of quantum jumps. However, these frameworks predominantly focus on weak Markovian interactions, neglecting the potentially crucial role of memory effects. To address this, we investigate, utilizing the powerful hierarchical equations of motion method, how a non-Markovian environment can modify the Liouvillian skin effect. We demonstrate that a non-Markovian environment can induce a “thick skin effect,” where the skin mode broadens and shifts into the bulk. We further identify that the skin-mode quantum coherence can only be generated when the coupling contains counter-rotating terms, leading to the coherence delocalization and oscillatory relaxation with a characteristic linear scaling with system size. Remarkably, both the skin-mode and steady-state coherence exhibit resistance to decoherence from additional environmental noise. These findings highlight the profound impact of system-bath correlations on relaxation and localization, revealing unique phenomena beyond conventional Markovian approximations.
We unveil a quantum Pontus-Mpemba effect enabled by the Liouvillian skin effect in a dissipative tight-binding chain with asymmetric incoherent hopping and coherent boundary coupling. The skin effect, induced by non-reciprocal dissipation, localizes relaxation modes near the system boundaries and gives rise to non-orthogonal spectral geometry. While such non-normality is often linked to slow relaxation, we show that it can instead accelerate relaxation through a two-step protocol - realizing a quantum Pontus-Mpemba effect. Specifically, we consider a one-dimensional open chain with coherent hopping J, asymmetric incoherent hoppings JR=JL, and a controllable end-to-end coupling ε. For ε=0, the system exhibits the Liouvillian skin effect, with left and right eigenmodes localized at opposite edges. We compare two relaxation protocols toward the same stationary state: (i) a direct relaxation with ε=0, and (ii) a two-step (Pontus) protocol where a brief coherent evolution transfers the excitation across the lattice before relaxation. Although both share the same asymptotic decay rate, the two-step protocol relaxes significantly faster due to its reduced overlap with the slow boundary-localized Liouvillian mode. The effect disappears when JR=JL, i.e., when the skin effect vanishes. Our results reveal a clear connection between boundary-induced non-normality and protocol-dependent relaxation acceleration, suggesting new routes for controlling dissipation and transient dynamics in open quantum systems.
The non-Hermitian skin effect (NHSE) refers to the accumulation of an extensive number of eigenstates at system boundaries under open boundary conditions (OBCs). As a dynamical consequence, wave packets in such systems drift and ultimately accumulate at a boundary, giving rise to the dynamical skin effect (DSE). While strong quasiperiodic potentials are known to suppress the DSE by inducing localization, we show that the introduction of Ornstein-Uhlenbeck (OU) noise unexpectedly restores it. Using perturbative analysis, we demonstrate that noise effectively maps the non-Hermitian Schrödinger dynamics onto a non-reciprocal master equation, whose complex spectrum develops a noise-induced point gap. This mechanism enables delocalization, reinstates directional transport, and revives the DSE even in regimes where the static NHSE is absent. Moreover, the relaxation dynamics exhibit a non-monotonic dependence on noise strength, reflecting a competition between noise-assisted delocalization and noise-induced decoherence. Our results uncover a noise-enabled mechanism for resurrecting the DSE and suggest a new route for controlling transport in quasiperiodic, open quantum systems.
Non-Hermitian skin effect is one of the most captivating phenomena in non-Hermitian systems, characterized by the extensive localization of eigenstates near open boundaries. In its conventional form, the localization length of a skin mode is independent of the system size. Remarkably, however, when the open boundaries are coupled to realize a generalized boundary condition, the localization length can undergo a drastic transformation, becoming proportional to the system length. This intriguing regime is known as the scale-free skin effect (SFSE). Although SFSE has been observed in numerous one-dimensional non-Hermitian models through case-by-case studies, a unified theoret ical framework capable of predicting its emergence and characteristic properties remains absent. In this work, we take a firm step forward by establishing a model-independent framework for the ana lytic determination of scale-free localization lengths in certain regimes. Our key insight is to treat generalized boundary conditions as a perturbation of the periodic boundary conditions, thereby circumventing the singular response-to-perturbation that would otherwise arise if they were pertur batively treated relative to open boundary conditions. Our work sheds new light on understanding SFSE in non-Hermitian systems.
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.
Non-Hermitian systems with globally reciprocal couplings -- such as the Hatano-Nelson model with stochastic imaginary gauge fields -- avoid the conventional non-Hermitian skin effect, displaying erratic bulk localization while retaining ballistic transport. An open question is whether similar behavior arises when non-reciprocity originates at the Liouvillian level rather than from an effective non-Hermitian Hamiltonian obtained via post-selection. Here, a lattice model with globally reciprocal Liouvillian dynamics and locally asymmetric incoherent hopping is investigated, a disordered setting in which Liouvillian-specific effects have remained largely unexplored. While the steady state again shows disorder-dependent, erratic localization without boundary accumulation, {\color{black}excitations in the incoherent-hopping regime spread via {\em Sinai-type subdiffusion}, dramatically slower than ordinary diffusion in symmetric stochastic lattices.} {\color{black}This highlights that the genuinely distinct Liouvillian signature is the coexistence of global reciprocity with ultra-slow, disorder-induced subdiffusive transport, rather than the erratic localization itself.} {\color{black}These results reveal a fundamental distinction between globally reciprocal Hamiltonian and Liouvillian systems: in both cases the skin effect is suppressed, but only in Liouvillian dynamics erratic skin localization can coexist with subdiffusive transport
Recent years have seen remarkable development in open quantum systems effectively described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological systems is the skin effect, anomalous localization of an extensive number of eigenstates driven by nonreciprocal dissipation. Despite its significance for non-Hermitian topological phases, the relevance of the skin effect to quantum entanglement and critical phenomena has remained unclear. Here, we find that the skin effect induces a nonequilibrium quantum phase transition in the entanglement dynamics. We show that the skin effect gives rise to a macroscopic flow of particles and suppresses the entanglement propagation and thermalization, leading to the area law of the entanglement entropy in the nonequilibrium steady state. Moreover, we reveal an entanglement phase transition induced by the competition between the unitary dynamics and the skin effect even without disorder or interactions. This entanglement phase transition accompanies nonequilibrium quantum criticality characterized by a nonunitary conformal field theory whose effective central charge is extremely sensitive to the boundary conditions. We also demonstrate that it originates from an exceptional point of the non-Hermitian Hamiltonian and the concomitant scale invariance of the skin modes localized according to the power law. Furthermore, we show that the skin effect leads to the purification and the reduction of von Neumann entropy even in Markovian open quantum systems described by the Lindblad master equation. Our work opens a way to control the entanglement growth and establishes a fundamental understanding of phase transitions and critical phenomena in open quantum systems far from thermal equilibrium.