Lindbladian versus Postselected non-Hermitian Topology

Area of Science:

• Quantum Physics
• Condensed Matter Physics
• Topological Matter

Background:

• Non-Hermitian Hamiltonians are typically analyzed using pure quantum states, which decay or grow over time.
• Many-body systems with loss and gain are better described by mixed-state open quantum dynamics.
• Postselection of measurement outcomes is required to map mixed-state dynamics to pure-state non-Hermitian dynamics, but becomes computationally expensive with increasing particle number.

Purpose of the Study:

• To investigate the survival of non-Hermitian topology, specifically the non-Hermitian skin effect and its relation to bulk winding numbers, in one spatial dimension without postselection.
• To define and analyze the winding number of the Lindbladian superoperator for quadratic fermion systems.
• To compare the Lindbladian winding number with the winding number of the associated postselected non-Hermitian Hamiltonian.

Main Methods:

• Definition of the winding number for Lindbladian superoperators in quadratic fermion systems.
• Systematic comparison between Lindbladian winding numbers and postselected non-Hermitian Hamiltonian winding numbers.
• Analysis of phase transitions in systems with both loss and gain.

Main Results:

• The winding numbers of the Lindbladian superoperator and the postselected non-Hermitian Hamiltonian are proven to be equal (opposite) in the absence of gain (loss).
• A physical explanation for the relationship between these winding numbers is provided.
• In the presence of both loss and gain, the Lindbladian winding number remains quantized and non-zero, typically indicating a phase transition.
• This transition, marked by a reversal of the Lindbladian skin effect localization, is obscured by postselection.
• A scenario is identified where the removal of postselection induces a skin effect in topologically trivial non-Hermitian dynamics.

Conclusions:

• Non-Hermitian topology and the non-Hermitian skin effect can be robustly described by open quantum dynamics without postselection.
• Postselection can hide crucial topological phase transitions and phenomena in non-Hermitian systems.
• The Lindbladian winding number provides a valuable tool for characterizing topology in open quantum systems, even when postselection is not feasible.