Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model

Abstract

We numerically study the evolution of spectral correlations in the entanglement Hamiltonian (EH) of non-interacting fermions in the Aubry-André-Harper (AAH) model. We analyze the time evolution of the EH spectrum in a nonequilibrium setting by studying several quantities: spectral distribution, level statistics, entanglement entropy, and spectral form factor (SFF) in the context of the delocalization-localization transition in the AAH model. It is observed that the SFF of the entanglement spectrum in the delocalized phase and at the phase-transition point evolves in three-time intervals. We make a systematic study of the emergence of these three timescales for various initial states and find that the number of time intervals remains three unless the Hamiltonian is tuned in the localized phase or when the initial state is maximally entangled, then there is a featureless time evolution. We find a broad direct correlation between the entanglement entropy and the length of the ramp of the SFF. We also find that in the delocalized phase the spectral correlations are stronger in the center of the spectrum and grow progressively weaker as more and more of the spectrum is considered.

13 pages, 14 figures

References in corpus (15)

• Anderson Transitions
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Does scrambling equal chaos?
• Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories
• The entanglement membrane in chaotic many-body systems
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Universal spectral form factor for many-body localization
• Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
• Realistic many-body quantum systems vs full random matrices: static and dynamical properties
• Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains
• Spectral decoupling in many-body quantum chaos
• Quantum entanglement and the Born-Markov approximation for an open quantum system
• Entanglement statistics in Markovian open quantum systems: a matter of mutation and selection
• Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models
• Quench dynamics of entanglement spectrum and topological superconducting phases in a long-range Hamiltonian

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