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SUMMARY:Rigorous Lower Bounds on Spectral Gaps of Frustration-Free Quantum
  Spin Chains
DTSTART:20260717T124500Z
DTEND:20260717T140000Z
DTSTAMP:20260709T002300Z
UID:indico-event-16937@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Norbert Schuch (University of Vienna)\n\nI will pres
 ent some new results for obtaining rigorous lower bounds on the spectral g
 ap of frustration-free quantum spin chains. Such spin chains are character
 ized by the fact that their ground state minimizes each local Hamiltonian 
 term individually\, and include paradigmatic models such as the AKLT and t
 he Majumdar-Ghosh model. In my talk\, I will discuss two new results\, whi
 ch significantly improve upon existing methods: First\, a new approach bas
 ed on semidefinite programming to obtain rigorous lower bounds on the spec
 tral gap of frustration-free Hamiltonians. Second\, a method based on the 
 so-called "martingale method" of Fannes\, Nachtergaele\, and Werner\, whic
 h not only significantly improves upon their method\, but also results in 
 a much simplified proof of the fact that a large class of frustration-free
  Hamiltonians (namely\, parent Hamiltonians of well-conditioned Matrix Pro
 duct States) are always gapped.\n \nPour être informé des prochains sé
 minaires vous pouvez vous abonner à la liste de diffusion en écrivant un
  mail à sympa@listes.math.cnrs.fr avec comme sujet: "subscribe seminaire_
 physique PRENOM NOM"(indiquez vos propres prénom et nom) et laissez le co
 rps du message vide.\n\nhttps://indico.math.cnrs.fr/event/16937/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/16937/
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