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SUMMARY:Anurag Anshu (University of California\, Berkeley)
DTSTART:20210610T003000Z
DTEND:20210610T013000Z
DTSTAMP:20260423T041751Z
UID:UTSQSI/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UTSQSI/25/">
 An area law for 2D frustration-free spin systems</a>\nby Anurag Anshu (Uni
 versity of California\, Berkeley) as part of Centre for Quantum Software a
 nd Information Seminar Series\n\n\nAbstract\nWe prove that the entanglemen
 t entropy of the ground state of a locally gapped frustration-free 2D latt
 ice spin system satisfies an area law with respect to a vertical bipartiti
 on of the lattice into left and right regions. We first establish that the
  ground state projector of any locally gapped frustration-free 1D spin sys
 tem can be approximated to within error ∈ by a degree O(√nlog(∈-1)) 
 (equation unformatted-refer to paper link) multivariate polynomial in the 
 interaction terms of the Hamiltonian. This generalizes the optimal bound o
 n the approximate degree of the boolean AND function\, which corresponds t
 o the special case of commuting Hamiltonian terms. For 2D spin systems we 
 then construct an approximate ground state projector (AGSP) that employs t
 he optimal 1D approximation in the vicinity of the boundary of the biparti
 tion of interest. This AGSP has sufficiently low entanglement and error to
  establish the area law using a known technique.\n\nJoint work with Itai A
 rad and David Gosset. arXiv: 2103.02492 (https://arxiv.org/abs/2103.02492)
 \n\nTo request the zoom link\, please send a message cqsiadmin@uts.edu.au 
 using your business/organisation/institution email address.\nHosted by Ass
 ociate Professor Troy Lee\, Centre for Quantum Software and Information\, 
 University of Technology Sydney\n
LOCATION:https://researchseminars.org/talk/UTSQSI/25/
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