Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians

Patrycja Łydżba, Marcos Rigol, Lev Vidmar

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


The eigenstate entanglement entropy is a powerful tool to distinguish integrable from generic quantum-chaotic models. In integrable models, the average eigenstate entanglement entropy (over all Hamiltonian eigenstates) has a volume-law coefficient that generally depends on the subsystem fraction. In contrast, it is maximal (subsystem fraction independent) in quantum-chaotic models. Using random matrix theory for quadratic Hamiltonians, we obtain a closed-form expression for the average eigenstate entanglement entropy as a function of the subsystem fraction. We test it against numerical results for the quadratic Sachdev-Ye-Kitaev model and show that it describes the results for the power-law random banded matrix model (in the delocalized regime). We show that localization in quasimomentum space produces (small) deviations from our analytic predictions.

Original languageEnglish (US)
Article number180604
JournalPhysical review letters
Issue number18
StatePublished - Oct 27 2020

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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