BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//6.4.7.2//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:0-976@lptms.universite-paris-saclay.fr DTSTART;TZID=Europe/Paris:20241011T134500 DTEND;TZID=Europe/Paris:20241011T151500 DTSTAMP:20241004T080350Z URL:http://www.lptms.universite-paris-saclay.fr/seminars/informal-quantum- seminar-luca-capizzi-lptms/ SUMMARY:Informal Quantum Seminar: Luca Capizzi (LPTMS) - Salle des séminai res du FAST et du LPTMS\, bâtiment Pascal n°530 - 11 Oct 24 13:45 DESCRIPTION:GROUND STATES OF QUANTUM MANY-BODY SYSTEMS AND EXPONENTIAL DECA Y OF CORRELATIONS \n \;\nLuca Capizzi (LPTMS)\n\n\nGround states of q uantum many-body systems are known to have qualitatively distinct properti es compared to eigenstates in the middle of the spectrum. Specifically\, i n the presence of a finite energy gap\, while the latter display volume-la w entanglement\, the former show area-law entanglement\; in other words\, the ground-state entanglement entropy of a subregion scales with its area. As a consequence\, these states can be efficiently simulated using state- of-the-art numerical tensor network methods\, such as Matrix Product State s (MPS). This fundamental result of modern quantum physics traces back to a series of mathematical theorems proven by M.B. Hastings at the beginning of this century [1-3]. In this seminar\, based on Ref. [1]\, I will show how a gap in the energy spectrum implies an exponential decay of spatial c orrelations\, a highly non-trivial result obtained via the Lieb-Robinson b ound and energy filters. Furthermore\, I will emphasize that having short- range correlations\, a property that holds generically even in the middle of the energy spectrum [4]\, does not directly relate to area-law entangle ment.\n\n\n\n\n\n[1] M. B. Hastings\, Locality in Quantum and Markov Dynam ics on Lattices and Networks\, Phys. Rev. Lett. 93\, 140402 (2004).\n[2] M . B. Hastings\, An Area Law for One Dimensional Quantum Systems\, JSTAT\, P08024 (2007).\n[3] M. B. Hastings\, Entropy and entanglement in quantum g round states\, Phys. Rev. B 76\, 035114 (2007).\n[4] Araki\, H. Gibbs stat es of a one dimensional quantum lattice\, Commun.Math. Phys. 14\, 120–15 7 (1969).\n CATEGORIES:seminars LOCATION:Salle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°53 0\, rue André Riviere\, Orsay\, 91405\, France X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Riviere\, Orsay\ , 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Salle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°530:geo:0,0 END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:DAYLIGHT DTSTART:20240331T030000 TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST END:DAYLIGHT END:VTIMEZONE END:VCALENDAR