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UID:0-993@lptms.universite-paris-saclay.fr
DTSTART;TZID=Europe/Paris:20241108T134500
DTEND;TZID=Europe/Paris:20241108T151500
DTSTAMP:20241107T112714Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/informal-quantum-
 seminar-du-lptms-luca-capizzi-lptms/
SUMMARY:Informal Quantum Seminar du LPTMS: Luca Capizzi  (LPTMS) - Salle de
 s séminaires du FAST et du LPTMS\, bâtiment Pascal n°530 - 8 Nov 24 13:
 45
DESCRIPTION:Ground states of quantum many-body systems and exponential deca
 y of correlations \n\nLuca Capizzi (LPTMS)\n\n\n\nGround states of quantu
 m many-body systems are known to have qualitatively distinct properties co
 mpared to eigenstates in the middle of the spectrum. Specifically\, in the
  presence of a finite energy gap\, while the latter display volume-law ent
 anglement\, the former show area-law entanglement\; in other words\, the g
 round-state entanglement entropy of a subregion scales with its area. As a
  consequence\, these states can be efficiently simulated using state-of-th
 e-art numerical tensor network methods\, such as Matrix Product States (MP
 S). This fundamental result of modern quantum physics traces back to a ser
 ies of mathematical theorems proven by M.B. Hastings at the beginning of t
 his 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 correl
 ations\, a highly non-trivial result obtained via the Lieb-Robinson bound 
 and energy filters. Furthermore\, I will emphasize that having short-range
  correlations\, a property that holds generically even in the middle of th
 e energy spectrum [4]\, does not directly relate to area-law entanglement.
 \n\n[1] M. B. Hastings\, Locality in Quantum and Markov Dynamics on Lattic
 es 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 ground states\
 , Phys. Rev. B 76\, 035114 (2007).\n[4] Araki\, H. Gibbs states of a one d
 imensional quantum lattice\, Commun.Math. Phys. 14\, 120–157 (1969).\n\n
 &nbsp\;\n\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
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