Thermalization in Krylov Basis
arXiv:2403.06655 · doi:10.1140/epjc/s10052-025-13757-2
Abstract
We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific tridiagonal form with all other elements in the matrix are exponentially small, reminiscent of the eigenstate thermalization hypothesis. Within this framework, we propose that the nature of thermalization, whether weak or strong, can be examined by the infinite time average of the Krylov complexity. Moreover, we analyze the variance of Lanczos coefficients as another probe for the nature of thermalization. One observes that although the variance of Lanczos coefficients may capture certain features of thermalization, it is not as effective as the infinite time average of complexity.
14 pages, 14 figures. v2:Refs added, comments added, more explanation on Krylov basis thermalization hypothesis added. v2: Updated to match the published version
References in corpus (24)
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- The approach to thermal equilibrium in quantized chaotic systems
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Strong and weak thermalization of infinite non-integrable quantum systems
- A Universal Operator Growth Hypothesis
- Quantum chaos and the complexity of spread of states
- Quantum equilibration in finite time
- Operator complexity: a journey to the edge of Krylov space
- On The Evolution Of Operator Complexity Beyond Scrambling
- Krylov complexity from integrability to chaos
- Toda chain flow in Krylov space
- Krylov Localization and suppression of complexity
- Operator growth and Krylov construction in dissipative open quantum systems
- Universal chaotic dynamics from Krylov space
- Euclidean operator growth and quantum chaos
- Probing quantum scars and weak ergodicity-breaking through quantum complexity
- On Krylov complexity in open systems: an approach via bi-Lanczos algorithm
- Quasiparticle explanation of "weak thermalization" regime under quench in a non-integrable quantum spin chain
- Krylov Complexity in Quantum Field Theory
- Spectral and Krylov Complexity in Billiard Systems
- A universal approach to Krylov State and Operator complexities
- State Dependence of Krylov Complexity in CFTs
- Assessing the saturation of Krylov complexity as a measure of chaos
- Quantum information scrambling in the presence of weak and strong thermalization
Cited by in corpus (10)
- Quantum Dynamics in Krylov Space: Methods and Applications
- Krylov fractality and complexity in generic random matrix ensembles
- Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
- Krylov Complexity as a Probe for Chaos
- Streamlined Krylov construction and classification of ergodic Floquet systems
- Properties of Krylov state complexity in qubit dynamics
- Krylov Complexity Meets Confinement
- Krylov Complexity in Lifshitz-type Dirac Field Theories
- ScarFinder: a detector of optimal scar trajectories in quantum many-body dynamics
- Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory