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SUMMARY:Representing many-body wave functions using Gaussian processes - A
 ldo Glielmo\, International School for Advanced Studies (SISSA)
DTSTART:20200525T153000Z
DTEND:20200525T160000Z
UID:TALK142555@talks.cam.ac.uk
CONTACT:Bingqing Cheng
DESCRIPTION:The dimension of the Fock space of N electrons grows exponenti
 ally with N\, and developing compact representations that can capture the 
 most important correlations of many-body wave functions with polynomial re
 sources is hence a necessity. Traditional representations (as for instance
  the Gutzwiller\, the Jastrow\, and the EPS) directly reproduce a specific
  set of low-order correlations that are deemed important. Conversely\, par
 ameterisations based on the use of neural networks (NN) architectures have
  no clear physical interpretation\, nonetheless they attracted a lot of at
 tention for their formal systematic improvability.\n  In my talk I will pr
 esent “Gaussian process states” (GPS)\, a novel framework for the cons
 truction of many-body states based on Bayesian statistics and Gaussian pro
 cess (GP) regression. Similarly to a NN representation\, GPS possesses the
  “universal approximator” property but\, differently from it\, can be 
 interpreted in terms of physically meaningful correlations. For instance\,
  under specific limits a GPS is able to exactly reproduce Gutzwiller\, Jas
 trow and EPS wave functions.\n  I will introduce two numerical approaches 
 to train a GPS: a “fragmentation” approach\, and direct variational op
 timisation. Extensive benchmarking on the Fermionic Hubbard model in 1 and
  2 spatial dimensions reveals the competitiveness of the GPS framework\, w
 hich is found to achieve similar and often superior descriptions of correl
 ated quantum problems than existing state-of-the-art approaches.
LOCATION:virtual ZOOM meeting ID: 263 591 6003\, https://zoom.us/j/2635916
 003
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