PIRSA:20030015

Video URL

https://pirsa.org/20030015

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

Rigol, M. (2020). Entanglement entropy of highly excited eigenstates of many-body lattice Hamiltonians. Perimeter Institute for Theoretical Physics. https://pirsa.org/20030015

Rigol, Marcos. Entanglement entropy of highly excited eigenstates of many-body lattice Hamiltonians. Perimeter Institute for Theoretical Physics, Mar. 04, 2020, https://pirsa.org/20030015 

          @misc{ scivideos_PIRSA:20030015,
            doi = {10.48660/20030015},
            url = {https://pirsa.org/20030015},
            author = {Rigol, Marcos},
            keywords = {Quantum Matter, Other Physics},
            language = {en},
            title = {Entanglement entropy of highly excited eigenstates of many-body lattice Hamiltonians},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2020},
            month = {mar},
            note = {PIRSA:20030015 see, \url{https://scivideos.org/index.php/pirsa/20030015}}
          }

Marcos Rigol Pennsylvania State University

Talk numberPIRSA:20030015
DOI10.48660/20030015
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

The average entanglement entropy of subsystems of random pure states is (nearly) maximal. In this talk, we discuss the average entanglement entropy of subsystems of highly excited eigenstates of integrable and nonintegrable many-body lattice Hamiltonians. 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 entropy exhibits a leading volume-law term that is different from that of random pure states. We argue that such a leading term is likely universal for translationally invariant (noninteracting and interacting) integrable models. For random pure states with a fixed particle number (random canonical states) away from half filling and normally distributed real coefficients, we prove that the deviation from the maximal value grows with the square root of the system's volume when the size of the subsystem is one half of that of the system. We then show that the average entanglement entropy of highly excited eigenstates of a particle number conserving quantum chaotic model is the same as that of random canonical states.