Entanglement entropy of highly excited eigenstates of many-body lattice Hamiltonians

The average entanglement entropy of subsystems of random pure states is (nearly) maximal [1]. In this talk, we discuss how the average entanglement entropy of subsystems of highly excited eigenstates of integrable and nonintegrable many-body lattice Hamiltonians (with a conservation law) differ from that of random pure states. For translationally invariant quadratic models (or spin models mappable to them) we prove that, when the subsystem size is not a vanishing fraction of the entire system, the average eigenstate entanglement exhibits a leading volume-law term that is different from that of random pure states [2]. We argue that such a leading term is universal for translationally invariant quadratic models [3] and, likely, also for interacting integrable models [4]. For highly excited eigenstates of a particle-number-conserving quantum chaotic model away from half filling, we find that the deviation from the maximal value grows with the square root of the system's volume, when 1/2 of the system is traced out. Such a deviation is proved to occur in random pure states with a fixed particle number and normally distributed real coefficients [5].

References:
[1] D. N. Page, Phys. Rev. Lett. 71, 1291 (1993).
[2] L. Vidmar, L. Hackl, E. Bianchi, and M. Rigol. Phys. Rev. Lett. 119, 020601 (2017).
[3] L. Vidmar, L. Hackl, E. Bianchi, and M. Rigol. Phys. Rev. Lett. 121, 220602 (2018).
[4] T. LeBlond, K. Mallayya, L. Vidmar, and M. Rigol, arXiv:1909.09654 (to appear in Phys. Rev. E).
[5] L. Vidmar and M. Rigol. Phys. Rev. Lett. 119, 220603 (2017).