Lindbladian versus postselected non-hermitian topology
File(s)
Published version
Author(s)
Chaduteau, Alexandre
Lee, Derek KK
Schindler, Frank
Type
Journal Article
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.
Date Issued
2026-01-09
Date Acceptance
2025-12-16
Citation
Physical Review Letters, 2026, 136 (1)
ISSN
0031-9007
Publisher
American Physical Society (APS)
Journal / Book Title
Physical Review Letters
Volume
136
Issue
1
Copyright Statement
Published by the American Physical Society Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
License URL
Publication Status
Published
Article Number
016603
Date Publish Online
2026-01-06