Lindbladian versus Postselected Non-Hermitian Topology

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Chaduteau, Alexandre, Lee, Derek K. K., Schindler, Frank
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908751592685568
author Chaduteau, Alexandre
Lee, Derek K. K.
Schindler, Frank
author_facet Chaduteau, Alexandre
Lee, Derek K. K.
Schindler, Frank
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_07187
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Lindbladian versus Postselected Non-Hermitian Topology
Chaduteau, Alexandre
Lee, Derek K. K.
Schindler, Frank
Quantum Physics
Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
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.
title Lindbladian versus Postselected Non-Hermitian Topology
topic Quantum Physics
Mesoscale and Nanoscale Physics
Strongly Correlated Electrons
url https://arxiv.org/abs/2507.07187