Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
arXiv:2101.11236 · doi:10.1103/PhysRevResearch.3.043060
Abstract
In this letter we point out that the Lindblad spectrum of a quantum many-body system displays a segment structure and exhibits two different energy scales in the strong dissipation regime. One energy scale determines the separation between different segments, being proportional to the dissipation strength, and the other energy scale determines the broadening of each segment, being inversely proportional to the dissipation strength. Ultilizing a relation between the dynamics of the second Rényi entropy and the Lindblad spectrum, we show that these two energy scales respectively determine the short- and the long-time dynamics of the second Rényi entropy starting from a generic initial state. This gives rise to opposite behaviors, that is, as the dissipation strength increases, the short-time dynamics becomes faster and the long-time dynamics becomes slower. We also interpret the quantum Zeno effect as specific initial states that only occupy the Lindblad spectrum around zero, for which only the broadening energy scale of the Lindblad spectrum matters and gives rise to suppressed dynamics with stronger dissipation. We illustrate our theory with two concrete models that can be experimentally verified.
5 pages, 4 figures
References in corpus (9)
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- PT-symmetric quantum Liouvillian dynamics
- Many-body Hierarchy of Dissipative Timescales in a Quantum Computer
- Random generators of Markovian evolution: A quantum-classical transition by superdecoherence
- Solving the Liouvillian Gap with Artificial Neural Networks
- Full spectrum of the Liouvillian of open dissipative quantum systems in the Zeno limit
- Perturbative calculations of entanglement entropy
- Page Curve from Non-Markovianity
- Entropy Linear Response Theory with Non-Markovian Bath
Cited by in corpus (18)
- Quantum Dynamics in Krylov Space: Methods and Applications
- Non-Hermitian skin effect in one-dimensional interacting Bose gas
- Encircling the Liouvillian exceptional points: a brief review
- Quasiparticles of Decoherence Processes in Open Quantum Many-Body Systems: Incoherentons
- Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
- Exact solution of the boundary-dissipated transverse field Ising model: Structure of Liouvillian spectrum and dynamical duality
- Universal Properties of the Spectral Form Factor in Open Quantum Systems
- Decoherence rate in random Lindblad dynamics
- Operator size growth in Lindbladian SYK
- Dynamical Signatures of Liouvillian Flat Band
- Initial-state-dependent quantum speed limit for dissipative state preparation: Framework and optimization
- Fate of dissipative hierarchy of timescales in the presence of unitary dynamics
- Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
- Dynamic transition of the density-matrix topology under parity-time symmetry
- Characterizing dynamical behaviors in topological open systems with boundary dissipations
- Separation of relaxation timescales via strong system-bath coupling: Dissipative three-level system as a case study
- Discovery of energy landscapes towards optimized quantum transport: Environmental effects and long-range tunneling
- Open-system dynamics in local Lindbladians with chaotic spectra