Typical eigenstate entanglement entropy as a diagnostic of quantum chaos and integrability

          @misc{ pirsa_PIRSA:24050040,
            doi = {10.48660/24050040},
            url = {https://pirsa.org/24050040},
            author = {Rigol, Marcos},
            keywords = {Quantum Information},
            language = {en},
            title = {Typical eigenstate entanglement entropy as a diagnostic of quantum chaos and integrability},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {may},
            note = {PIRSA:24050040 see, \url{https://pirsa.org}}
          }
          

Abstract

Quantum-chaotic systems are known to exhibit eigenstate thermalization and to generically thermalize under unitary dynamics. In contrast, quantum-integrable systems exhibit a generalized form of eigenstate thermalization and need to be described using generalized Gibbs ensembles after equilibration. I will discuss evidence that the entanglement properties of highly excited eigenstates of quantum-chaotic and quantum-integrable systems are fundamentally different. They both exhibit a typical bipartite entanglement entropy whose leading term scales with the volume of the subsystem. However, while the coefficient is constant and maximal in quantum- chaotic models, in integrable models it depends on the fraction of the system that is traced out. The latter is typical in random Gaussian pure states. I will also discuss the nature of the subleading corrections that emerge as a consequence of the presence of abelian and nonabelian symmetries in such models.