Journal article
Volume-Law Entanglement Entropy of Typical Pure Quantum States
E Bianchi, L Hackl, M Kieburg, M Rigol, L Vidmar
Prx Quantum | Published : 2022
Abstract
The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians has recently been conjectured to be a diagnostic of quantum chaos and integrability. In quantum chaotic systems it has been found to behave as in typical pure states, while in integrable systems it has been found to behave as in typical pure Gaussian states. In this tutorial, we provide a pedagogical introduction to known results about the entanglement entropy of subsystems of typical pure states and of typical pure Gaussian states. They both exhibit a leading term that scales with the volume of the subsystem, when smaller than one half of the volume of the system, but the prefactor of the volume ..
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Grants
Awarded by Javna Agencija za Raziskovalno Dejavnost RS
Funding Acknowledgements
We would like to thank Pietro Dona, Peter Forrester, Patrycja LydZba, Lorenzo Piroli, and Nicholas Witte for inspiring discussions. E.B. acknowledges support from the National Science Foundation, Grant No. PHY-1806428, and from the John Templeton Foundation via the ID 61466 grant, as part of the "Quantum Information Structure of Spacetime (QISS)" project (qiss.fr). L.H. gratefully acknowledges support from the Alexander von Humboldt Foundation. M.K. acknowledges support from the Australian Research Council (ARC) under Grant No. DP210102887. M.R. acknowledges support from the National Science Foundation under Grant No. 2012145. L.V. acknowledges support from the Slovenian Research Agency (ARRS), Research core fundings Grants No. P1-0044 and No. J1-1696. L.H. and M.K. are also grateful to the MATRIX Institute in Creswick for hosting the online research programme and workshop "Structured Random Matrices Downunder" (26 July-13 August 2021).