Lindbladian versus Postselected Non-Hermitian Topology
arXiv:2507.07187 · doi:10.1103/ljvt-w6hw
Abstract
The recent topological classification of non-Hermitian `Hamiltonians' is usually interpreted in terms of pure quantum states that decay or grow with time. However, many-body systems with loss and gain are typically better described by mixed-state open quantum dynamics, which only correspond to pure-state non-Hermitian dynamics upon a postselection of measurement outcomes. Since postselection becomes exponentially costly with particle number, we here investigate to what extent the most important example of non-Hermitian topology can survive without it: the non-Hermitian skin effect and its relationship to a bulk winding number in one spatial dimension. After defining the winding number of the Lindbladian superoperator for a quadratic fermion system, we systematically relate it to the winding number of the associated postselected non-Hermitian Hamiltonian. We prove that the two winding numbers are equal (opposite) in the absence of gain (loss), and provide a physical explanation for this relationship. When both loss and gain are present, the Lindbladian winding number typically remains quantized and non-zero, though it can change sign at a phase transition separating the loss and gain-dominated regimes. This transition, which leads to a reversal of the Lindbladian skin effect localization, is rendered invisible by postselection. We also identify a case where removing postselection induces a skin effect from otherwise topologically trivial non-Hermitian dynamics.
https://link.aps.org/doi/10.1103/ljvt-w6hw
References in corpus (52)
- Topological Insulators
- Edge states and topological invariants of non-Hermitian systems
- Non-Hermitian Physics
- Localization transitions in non-Hermitian quantum mechanics
- Topological phases of non-Hermitian systems
- Symmetry and Topology in Non-Hermitian Physics
- Topological Origin of Non-Hermitian Skin Effects
- Quantum trajectories and open many-body quantum systems
- Zoo of quantum-topological phases of matter
- Non-Hermitian Boundary Modes
- Non-Hermitian skin effect and chiral damping in open quantum systems
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Non-Hermitian topological phenomena: A review
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Topology by dissipation
- Tenfold Way for Quadratic Lindbladians
- Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
- Topological framework for directional amplification in driven-dissipative cavity arrays
- Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
- Spectral theorem for the Lindblad equation for quadratic open fermionic systems
- Topology of density matrices
- Probing the topology of density matrices
- Non-equilibrium stationary states of quantum non-Hermitian lattice models
- Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
- Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations
- Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems
- Liouvillian Skin Effect in an Exactly Solvable Model
- Dislocation Non-Hermitian Skin Effect
- Equivalence of the effective non-hermitian Hamiltonians in the context of open quantum systems and strongly-correlated electron systems
- Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
- Exact solutions of interacting dissipative systems via weak symmetries
- Hermitian Bulk -- Non-Hermitian Boundary Correspondence
- Homotopy, Symmetry, and Non-Hermitian Band Topology
- Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification
- Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
- Hermitian and Non-Hermitian Topology from Photon-Mediated Interactions
- 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
- Bridging the gap between topological non-Hermitian physics and open quantum systems
- Topological phase transitions at finite temperature
- Effect of quantum jumps on non-Hermitian system
- Accelerating Relaxation Dynamics in Open Quantum System with Liouvillian Skin Effect
- Boundary sensitive Lindbladians and relaxation dynamics
- Skin Effect in Quadratic Lindbladian Systems: an Adjoint Fermion Approach
- Liouvillian skin effects and fragmented condensates in an integrable dissipative Bose-Hubbard model
- Observables in non-Hermitian systems: A methodological comparison
- Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
- Lindbladian dynamics with loss of quantum jumps
- Optical pumping through the Liouvillian skin effect
- Topological extension including quantum jump
- Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids