Despite recent intensive research on topological aspects of open quantum systems, effects of strong interactions have not been sufficiently explored. In this paper, we demonstrate that complex-valued interactions induce the Liouvillian skin effect by analyzing a one-dimensional correlated model with two-body loss. We show that, in the presence of complex-valued interactions, eigenmodes and eigenvalues of the Liouvillian strongly depend on boundary conditions. Specifically, we find that complex-valued interactions induce localization of eigenmodes of the Liouvillian around the right edge under open boundary conditions. To characterize the Liouvillian skin effect, we define the topological invariant by using the Liouvillian superoperator. Then, we numerically confirm that the topological invariant captures the Liouvillian skin effect. Furthermore, the presence of the localization of eigenmodes results in the unique dynamics observed only under open boundary conditions: particle accumulation at the right edge in transient dynamics. Our result paves the way to realize topological phenomena in open quantum systems induced by strong interactions.
Despite recent intensive research on topological aspects of open quantum systems, effects of strong interactions have not been sufficiently explored. In this paper, we demonstrate that complex-valued interactions induce the Liouvillian skin effect by analyzing a one-dimensional correlated model with two-body loss. We show that, in the presence of complex-valued interactions, eigenmodes and eigenvalues of the Liouvillian strongly depend on boundary conditions. Specifically, we find that complex-valued interactions induce localization of eigenmodes of the Liouvillian around the right edge under open boundary conditions. To characterize the Liouvillian skin effect, we define the topological invariant by using the Liouvillian superoperator. Then, we numerically confirm that the topological invariant captures the Liouvillian skin effect. Furthermore, the presence of the localization of eigenmodes results in the unique dynamics observed only under open boundary conditions: particle accumulation at the right edge in transient dynamics. Our result paves the way to realize topological phenomena in open quantum systems induced by strong interactions.
The non-Hermitian skin effect, in which eigenstates of non-Hermitian Hamiltonians are localized at one boundary in the open boundary condition, has attracted great interest recently. In this paper, we investigate the skin effect in one-dimensional dissipative quantum many-body systems, which we call the Liouvillian skin effect (LSE). We rigorously identify the existence of the LSE for generalized boundary conditions by solving the Liouvillian superoperator of an exactly solvable model with the advantage of the Bethe ansatz. The LSE is sensitive to boundary conditions where the signature is reflected in eigenfunctions of the system. We confirm that the LSE is fragile to a tiny coflow boundary hopping with non-Hermitian current but can survive a counterflow boundary hopping in the thermodynamic limit. Our work provides a prototypical example of exactly solvable dissipative quantum many-body lattice systems exhibiting the LSE for generalized boundary conditions. It can be further extended to other integrable open quantum many-body models.
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.
It has recently been established that open quantum systems may exhibit a strong spectral sensitivity to boundary conditions, known as the non-Hermitian/Liouvillian skin effect (NHSE/LSE), making the topological properties of the system boundary-condition sensitive. In this Letter, we ask the query: Can topological phase transitions of open quantum systems, captured by open boundary conditioned invariants, be observed in the dynamics of a system under periodic boundary conditions, even in the presence of NHSE/LSE? We affirmatively respond to this question, by considering the quench dynamics of entanglement spectrum in a periodic open quantum fermionic system. We demonstrate that the entanglement spectrum exhibits zero-crossings only when this periodic system is quenched from a topologically trivial to nontrivial phase, defined from the spectrum under open boundary conditions, even in systems featuring LSE. Our results reveal that non-Hermitian topological phases leave a distinctive imprint on the unconditional dynamics within a subsystem of fermionic systems.
Robust boundary states have been the focus of much recent research, both as topologically protected states and as non-Hermitian skin states. In this paper, we show that many-body effects can also induce analogs of these robust states in place of actual physical boundaries. Particle statistics or suitably engineered interactions, i.e., in ultracold atomic lattices can restrict the accessible many-body Hilbert space, and introduce effective boundaries in a spatially periodic higher-dimensional configuration space. We demonstrate the emergence of topological chiral modes in a two-fermion hopping model without open boundaries, with fermion pairs confined and asymmetrically propagated by suitably chosen fluxes. Heterogeneous nonreciprocal hoppings across different particle species can also result in robust particle clumping in a translation invariant setting, reminiscent of skin mode accumulation at an open boundary. But unlike fixed open boundaries, effective boundaries correspond to the locations of impenetrable particles and are mobile, giving rise to fundamentally different many-body versus single-body spectra and corresponding dynamics. Since nonreciprocal accumulation is agnostic to the dimensionality of restricted Hilbert spaces, our many-body skin states generalize directly in the thermodynamic limit. The many-body topological states, however, are nontrivially dimension-dependent, and their detailed exploration will stimulate further studies in higher dimensional topological invariants.
We investigate the impact of nonreciprocity on universality and critical phenomena in open quantum interacting many-body systems. Nonreciprocal open quantum systems often have an exotic spectral sensitivity to boundary conditions, known as the Liouvillian skin effect (LSE). By considering an open quantum XXZ spin chain that exhibits LSE, we demonstrate the existence of a universal scaling regime that is not affected by the presence of the LSE. We resolve the critical exponents, which differ from those of free fermions, via tensor network methods and demonstrate that observables exhibit a universal scaling collapse, irrespective of the reciprocity. We find that the LSE only becomes relevant when a healing length scale ξ_{heal} at the system's edge (which is different from the localization length of the eigenstate of the Liouvillian) exceeds the system size, allowing edge properties to dominate the physics. We expect this result to be a generic feature of nonreciprocal models in the vicinity of a critical point. The driven-dissipative quantum criticality we observe has no classical analog and stems from the existence of multiple dark states.
One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely, that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wave front. These phenomena are beyond the effective non-Hermitian Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged open quantum dynamics.