Neural-network quantum states for models of frustrated quantum magnets

 Abstract:
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.