Tenfold Way for Quadratic Lindbladians

Area of Science:

• Condensed Matter Physics
• Quantum Information Theory
• Topological Matter

Background:

• Topological classifications are well-established for closed quantum systems.
• Open quantum systems, interacting with their environment, present unique challenges.
• Lindblad master equations describe the dynamics of open quantum systems.

Purpose of the Study:

• To develop a topological classification for open fermionic systems.
• To investigate the nature and properties of topological edge states in these systems.
• To understand the influence of system-environment coupling on topological properties.

Main Methods:

• Formulation of quadratic Lindbladians for open fermionic systems.
• Representation of system dynamics using non-Hermitian single-particle matrices.
• Classification within ten non-Hermitian Bernard-LeClair symmetry classes.

Main Results:

• A topological classification for open fermionic systems governed by Lindblad equations is established.
• Topological edge excitations with finite lifetimes are predicted.
• These edge modes are shown to be independent of the steady-state properties.

Conclusions:

• The developed topological classification provides a new framework for open quantum systems.
• System-environment coupling significantly influences topological properties, potentially preserving or destroying existing classifications.
• The findings highlight the sensitivity of topological edge modes to the details of dissipation.