Signatures of quantum chaos transition in short spin chains

Abstract

The non-integrability of quantum systems, often associated with chaotic behavior, is a concept typically applied to cases with a high-dimensional Hilbert space Among different indicators signaling this behavior, the study of the long-time oscillations of the out-of-time-ordered correlator (OTOC) appears as a versatile tool, that can be adapted to the case of systems with a small number of degrees of freedom. Using such an approach, we consider the oscillations observed after the scrambling time in the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonance quantum simulator [J. Li,et al, Phys. Rev. X 7, 031011 (2017)]. We show that the systematic of the OTOC oscillations describes qualitatively well, in a chain with only 4 spins, the integrability-to-chaos transition inherited from the infinite chain.

6+ pages, 5 figures. Comments welcome

References in corpus (4)

• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Slow scrambling in disordered quantum systems
• Universal scrambling in gapless quantum spin chains

Cited by in corpus (16)

• Fingerprint of chaos and quantum scars in kicked Dicke model: An out-of-time-order correlator study
• Classical approach to equilibrium of out-of-time ordered correlators in mixed systems
• Effect of chaos on information gain in quantum tomography
• Relative asymptotic oscillations of the out-of-time-ordered correlator as a quantum chaos indicator
• Classical route to ergodicity and scarring in collective quantum systems
• Quantum Lyapunov exponent in dissipative systems
• Quantum chaos in the Dicke model and its variants
• Scaling at the OTOC Wavefront: free versus chaotic models
• Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems
• No-resonance conditions, random matrices, and quantum chaotic models
• Bipartite OTOC in open quantum systems: information scrambling and irreversibility
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
• Quantum Chaos in Non-Markovian Open Quantum Systems: Interferometric OTOC, Loschmidt Echo and Commutator Operator Norm
• Energy dynamics in a class of local random matrix Hamiltonians
• Quantum correlations in a cluster spin model with three-spin interactions
• Interferometric and Bipartite OTOC for Non-Markovian Open Quantum Spin-Chains and Lipkin-Meshkov-Glick Model