Assessing the saturation of Krylov complexity as a measure of chaos
arXiv:2212.06619 · doi:10.1103/PhysRevE.107.024217
Abstract
Krylov complexity is a novel approach to study how an operator spreads over a specific basis. Recently, it has been stated that this quantity has a long-time saturation that depends on the amount of chaos in the system. Since this quantity not only depends on the Hamiltonian but also on the chosen operator, in this work we study the level of generality of this hypothesis by studying how the saturation value varies in the integrability to chaos transition when different operators are expanded. To do this, we work with an Ising chain with a transverse-longitudinal magnetic field and compare the saturation of the Krylov complexity with the standard spectral measure of quantum chaos. Our numerical results show that the usefulness of this quantity as a predictor of the chaoticity is strongly dependent on the chosen operator.
7 pages, 8 figures
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Cited by in corpus (19)
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- Quantum Dynamics in Krylov Space: Methods and Applications
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- Thermalization in Krylov Basis
- Multiseed Krylov complexity
- Krylov Complexity of Open Quantum Systems: From Hard Spheres to Black Holes
- Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
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- Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit
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- Phase transitions in a non-Hermitian Su-Schrieffer-Heeger model via Krylov spread complexity
- Quantifying operator spreading and chaos in Krylov subspaces with quantum state reconstruction
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- Dependence of Krylov complexity on the initial operator and state
- Information acquisition, scrambling, and sensitivity to errors in quantum chaos
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