Liouvillian Skin Effect in an Exactly Solvable Model

Abstract

The interplay between dissipation, topology and sensitivity to boundary conditions has recently attracted tremendous amounts of attention at the level of effective non-Hermitian descriptions. Here we exactly solve a quantum mechanical Lindblad master equation describing a dissipative topological Su-Schrieffer-Heeger (SSH) chain of fermions for both open boundary condition (OBC) and periodic boundary condition (PBC). We find that the extreme sensitivity on the boundary conditions associated with the non-Hermitian skin effect is directly reflected in the rapidities governing the time evolution of the density matrix giving rise to a Liouvillian skin effect. This leads to several intriguing phenomena including boundary sensitive damping behavior, steady state currents in finite periodic systems, and diverging relaxation times in the limit of large systems. We illuminate how the role of topology in these systems differs in the effective non-Hermitian Hamiltonian limit and the full master equation framework.

arXiv comment21 pages, 13 figures, published

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Cited by in corpus (57)

• Topological Non-Hermitian skin effect
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Non-Hermitian Topological Phases: Principles and Prospects
• Non-Hermitian Mott Skin Effect
• Sensitivity of non-Hermitian systems
• Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations
• Anomalously large relaxation times in dissipative lattice models beyond the non-Hermitian skin effect
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Incoherent non-Hermitian skin effect in photonic quantum walks
• Absence of logarithmic and algebraic scaling entanglement phases due to skin effect
• Non-reciprocal dynamics and the non-Hermitian skin effect of repulsively bound pairs
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• Dissipative Boundary State Preparation
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• Steady-state edge burst: From free-particle systems to interaction-induced phenomena
• Dynamical Transition due to Feedback-induced Skin Effect
• Non-Hermitian extended midgap states and bound states in the continuum
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Non-Unitary Quantum Many-Body Dynamics using the Faber Polynomial Method
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Boundary sensitive Lindbladians and relaxation dynamics
• Liouvillian skin effects and fragmented condensates in an integrable dissipative Bose-Hubbard model
• Non-Markovian skin effect
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Multifractality of many-body non-Hermitian skin effect
• Exceptional points and exponential sensitivity for periodically driven Lindblad equations
• Lindbladian dynamics with loss of quantum jumps
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• The analytically tractable zoo of similarity-induced exceptional structures
• Higher-order Liouvillian exceptional points in the dissipative dynamics of quadratic fermions
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
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