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DESCRIPTION:PHYSICS SEMINAR\n\nTitle: Entanglement and separability of Rokh
 sar-Kivelson and resonating valence-bond states\n\nAbstract: Entanglement 
 and separability are two opposite yet intertwined notions in quantum mecha
 nics. A quantum state is said to be entangled if it is not separable\, and
  vice versa. Quantifying how entangled two subsystems are remains a challe
 nging problem\, which has led to important insights in the context of quan
 tum many-body systems. In this talk\, we discuss entanglement and separabi
 lity of dimer Rokhsar-Kivelson (RK) states and resonating valence-bond (RV
 B) states. For dimer RK states on general tilable graphs\, we prove the ex
 act separability of the reduced density matrix of two disconnected subsyst
 ems\, implying the absence of entanglement between the subsystems. For RVB
  states\, we show separability for disconnected subsystems up to exponenti
 ally small terms in the distance d between the two subsystems. We argue th
 at separability does hold in the scaling limit\, even for arbitrarily smal
 l ratio d/L\, where L is the characteristic size of the subsystems. Our re
 sults hold irrespective of the underlying graph (which include square and 
 triangular lattices)\, and hence suggest that separability (up to exponent
 ially small terms) between disjoint regions is a universal feature of RVB 
 states. In the case of adjacent subsystems for the RK states\, we derive e
 xact results for the logarithmic negativity in terms of partition function
 s of the underlying statistical model\, and recover the known result for t
 he Rényi-1/2 entropy in the limit of complementary subsystems.\n	Based on j
 oint work with Clément Berthier and William Witczak-Krempa\, arXiv: 2212.1
 1740\n\nCRM-Salle 4336-4384\, Pav. André Aisenstadt\n
DTSTART:20230207T203000Z
DTEND:20230207T213000Z
SUMMARY:Gillez Parez\, CRM-Université de Montréal
URL:/mathstat/channels/event/gillez-parez-crm-universi
 te-de-montreal-345747
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