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SUMMARY:The limits of Matrix Product States - Miguel Navascues\, Universit
 y of Vienna
DTSTART:20160421T131500Z
DTEND:20160421T141500Z
UID:TALK64391@talks.cam.ac.uk
CONTACT:Steve Brierley
DESCRIPTION:For the past twenty years\, Tensor Network States (TNS) have b
 een widely used to model the low energy sector of local  Hamiltonians. The
 ir success in doing so has led to the wide-held mantra that TNS of low bon
 d dimension are the `only physical states' of natural condensed matter sys
 tems. However\, given our experimental limitations to interact with such s
 ystems\, it is not clear how this conjecture translates into any observabl
 e effect. In this talk I will identify particular operational features per
 taining to all Matrix Product States (MPS)\, the class of TNS used to mode
 l non-critical one-dimensional spin chains. By exploiting two surprising s
 tructural constraints of MPS\, we see how to systematically derive `bond d
 imension witnesses'\, or k-local operators whose expectation value allows 
 us to lower bound the bond dimension of the underlying quantum state. We e
 xtend some of these results to the ansatz of Projected Entangled Pairs Sta
 tes (PEPS). As a bonus\, we use our insight on the structure of MPS to: a)
  derive some limitations on the use of MPS and PEPS for ground state energ
 y computations\; b) show how to decrease the complexity and boost the spee
 d of convergence of the semidefinite programming hierarchies described in 
 [Phys. Rev. Lett. 115\,\n020501 (2015)] for the characterization of finite
 -dimensional quantum correlations.\n
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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