Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians

• URL: http://arxiv.org/abs/2006.11302v2
• Date: Wed, 4 Nov 2020 09:52:56 GMT
• Title: Eigenstate Entanglement Entropy in Random Quadratic Hamiltonians
• Authors: Patrycja {\L}yd\.zba, Marcos Rigol, Lev Vidmar
• Abstract summary: In integrable models, the volume-law coefficient depends on the subsystem fraction. We show that the average entanglement entropy of eigenstates of the power-law random banded matrix model is close but not the same as the result for quadratic models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The eigenstate entanglement entropy has been recently shown to be a powerful tool to distinguish integrable from generic quantum-chaotic models. In integrable models, a unique feature of the average eigenstate entanglement entropy (over all Hamiltonian eigenstates) is that the volume-law coefficient depends on the subsystem fraction. Hence, it deviates from the maximal (subsystem fraction independent) value encountered 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 its correctness against numerical results for the quadratic Sachdev-Ye-Kitaev model. We also show that it describes the average entanglement entropy of eigenstates of the power-law random banded matrix model (in the delocalized regime), and that it is close but not the same as the result for quadratic models that exhibit localization in quasimomentum space.

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