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SUMMARY:Thermodynamics based on Neural Networks
DTSTART:20240718T121500Z
DTEND:20240718T134500Z
DTSTAMP:20241015T061300Z
UID:indico-event-168@indico.physik.uni-bielefeld.de
DESCRIPTION:Speakers: Daniel Wagner\n\n\n\n\nThe Variational Monte Carlo (
VMC) method has been used for decades to approximate the evolution of pure
states in quantum many-body physics. Several years ago\, (Artificial) Neu
ral Networks (A)NNs began to be considered as an ansatz for the variationa
l wave function taking advantage of their universal ability to approximate
functions in general. In this work\, three different NN algorithms to cal
culate thermodynamic properties are investigated as well as dynamic correl
ation functions at finite temperatures for the one- dimensional spin-1/2 H
eisenberg model. The first method is based on purification\, which allows
for the exact calculation of the operator trace. The second one is based o
n a sampling of the trace using minimally entangled states\, whereas the t
hird one utilizes quantum typicality. In the latter case\, we approximate
a typical infinite-temperature state by wave functions which are given by
a product of a projected pair and a NN part and evolve this typical state
in imaginary time. In the last part of this work\, the purification and th
e sampling method are applied to the two-dimensional J1-J2 model on the sq
uare lattice. Unfortunately\, computing accurate results for very low temp
eratures is difficult due to an increase in the rejection probability\, an
issue related to the Monte Carlo sampling and known as critical slowing d
own.\n\n\n\n\nhttps://indico.physik.uni-bielefeld.de/event/168/
LOCATION:D5-153 (UHG)
URL:https://indico.physik.uni-bielefeld.de/event/168/
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