Violation and Revival of Kramers' Degeneracy in Open Quantum Systems
arXiv:2108.05493 · doi:10.1103/PhysRevB.105.L241106
Abstract
Kramers' theorem ensures double degeneracy in the energy spectrum of a time-reversal symmetric fermionic system with half-integer total spin. Here we are now trying to go beyond the closed system and discuss Kramers' degeneracy in open systems out of equilibrium. In this letter, we prove that the Kramers' degeneracy in interacting fermionic systems is equivalent to the degeneracy in the spectra of different spins together with the vanishing of the inter-spin spectrum. We find the violation of Kramers' degeneracy in time-reversal symmetric open quantum systems is locked with whether the system reaches thermal equilibrium. After a sudden coupling to an environment in a time-reversal symmetry preserving way, the Kramers doublet experiences an energy splitting at a short time and then a recovery process. We verified the violation and revival of Kramers' degeneracy in a concrete model of interacting fermions and we find Kramers' degeneracy is restored after the local thermalization time. By contrast, for time-reversal symmetry with , we find although there is a violation and revival of spectral degeneracy for different spins, the inter-spin spectral function is always nonzero. We also prove that the degeneracy in spectral function protected by unitary symmetry can be maintained always.
arXiv comment5 pages, 3 figures
References in corpus (33)
- Quantum Spin Hall Effect in Graphene
- Topological Photonics
- Chaos and Quantum Thermalization
- A bound on chaos
- Quantum Spin Hall Effect
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Comments on the Sachdev-Ye-Kitaev model
- Exceptional Topology of Non-Hermitian Systems
- Symmetry and Topology in Non-Hermitian Physics
- Atomic quantum gases in periodically driven optical lattices
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
- A strongly correlated metal built from Sachdev-Ye-Kitaev models
- Solvable model for a dynamical quantum phase transition from fast to slow scrambling
- Many-body chaos at weak coupling
- Notes on the complex Sachdev-Ye-Kitaev model
- Quantum quench of the Sachdev-Ye-Kitaev Model
- Non-Hermitian Linear Response Theory
- Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization
- Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model
- Dispersive SYK model: band structure and quantum chaos
- Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
- Replica wormhole and information retrieval in the SYK model coupled to Majorana chains
- Evaporation dynamics of the Sachdev-Ye-Kitaev model
- Periodically Driven Sachdev-Ye-Kitaev Models
- Fragility of Time-Reversal Symmetry Protected Topological Phases
- Universal Constraints on Energy Flow and SYK Thermalization
- Stability of Time-Reversal Symmetry Protected Topological Phases
- An obstacle to sub-AdS holography for SYK-like models
- Kramers' degeneracy for open systems in thermal equilibrium
- Symmetry protected topological edge modes and emergent partial time reversal symmetry breaking in open quantum many-body systems
- Disconnecting a Traversable Wormhole: Universal Quench Dynamics in Random Spin Models
- Elastic backscattering of quantum spin Hall edge modes from Coulomb interactions with non-magnetic impurities