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SUMMARY:Locality at the boundary implies gap in the bulk for 2D PEPS - Mic
 hael Kastoryano
DTSTART:20180301T141500Z
DTEND:20180301T151500Z
UID:TALK102286@talks.cam.ac.uk
CONTACT:Johannes Bausch
DESCRIPTION:Proving that the parent Hamiltonian of a Projected Entangled P
 air State (PEPS) is gapped remains an important open problem. We take a st
 ep forward in solving this problem by showing that if the boundary state o
 f any rectangular subregion is a Gibbs state of a local Hamiltomian on the
  virtual indices with interactions decaying faster than exponentially in t
 he distance\, then the parent Hamiltonian of the bulk 2D PEPS has a consta
 nt gap in the thermodynamic limit. The proof employs the martingale method
  of nearly commuting projectors\, and exploits a result of Araki on the ro
 bustness of one dimensional Gibbs states. Our result provides one of the f
 irst rigorous connections between boundary theories and dynamical properti
 es in an interacting many body system. If time permits\, we will discuss s
 ome recent work on relating PEPS to certain O(n) Loop models.\n
LOCATION:MR11\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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