Martin Žonda » Neural-network quantum states for models of frustrated quantum magnets

KFKL CUNI CZ

Dr. Martin Žonda

Note, that the seminar will be held  at the Academy of Sciences:

Department of Condensed Matter Theory FZÚ AV ČR,
main lecture hall, Na Slovance 2, Praha 8

Location: Department of Condensed Matter Theory FZÚ AV ČR, main lecture hall, Na Slovance 2, Praha 8

In my talk I will introduce the concept of neural-network quantum states
(NQSs) used as variational functions in Monte Carlo studies of lattice
spin systems. In the first part of the presentation I will talk about
some basic principles of the method, the general motivation to use these
non-standard variational functions, as well as about their relation with
machine learning techniques. In the second part of the talk I will
discuss some of our recent results.

We have utilized NQS to investigate the ground state properties of the
Heisenberg model on a Shastry-Sutherland lattice. Here our main goal was
to show that a relatively simple NQS can be used to approximate the
ground-state of this model in its different phases. We have first
benchmarked several types of NQS with each other on small lattices and
compared their variational energies with the exact diagonalization
results. We argue that when precision, generality and computational
costs are taken into account, a good choice for addressing larger
systems is a simple restricted Boltzmann machine NQS. We have shown
that such NQS can describe all main phases of the investigated model in
zero magnetic field. We have also demonstrated that it can be utilized
to identify the point of phase transition between two different ordered
states. Moreover, NQS based on a restricted Boltzmann machine correctly
describes the intriguing plateaus forming in magnetization of the model
as function of the increasing magnetic field. These steps are a well
known property of various real materials with Shastry-Sutherland
topology.