Topological fingerprints in Liouvillian gaps.

Area of Science:

• Condensed Matter Physics
• Quantum Information Theory
• Many-Body Physics

Background:

• Topology in many-body physics is typically associated with equilibrium quantum states.
• Open quantum systems offer a new paradigm for observing topological phenomena.
• The Kitaev chain model serves as a fundamental system with distinct topological phases.

Purpose of the Study:

• To investigate the emergence of topological fingerprints in the relaxation dynamics of open quantum systems.
• To analyze the behavior of the Liouvillian gap in the Kitaev chain model under varying dissipation strengths.
• To establish a connection between topological phases and dissipative properties.

Main Methods:

• Modeling an open quantum system using the Kitaev chain with introduced dissipation.
• Calculating the Liouvillian gap in both strong and weak dissipative regimes.
• Analyzing the influence of superconducting pairing and chemical potential on the Liouvillian gap.

Main Results:

• A non-zero superconducting pairing opens a persistent Liouvillian gap, independent of system size.
• In strong dissipation, the Liouvillian gap is largely insensitive to the Hamiltonian's ground state topology.
• Weak dissipation reveals a crucial role for topology, making the gap immune to chemical potential changes in the topological phase.

Conclusions:

• Topological properties can be imprinted on the relaxation rates of open quantum systems.
• The Liouvillian gap serves as a sensitive indicator of topological phases, particularly under weak dissipation.
• Dissipation provides a tunable knob to probe and potentially control topological states in quantum matter.