Thermodynamics based on Neural Networks

by Daniel Wagner

Thursday Jul 18, 2024, 2:15 PM → 3:45 PM Europe/Berlin

D5-153 (UHG)

The 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) Neural Networks (A)NNs began to be considered as an ansatz for the variational wave function taking advantage of their universal ability to approximate functions in general. In this work, three different NN algorithms to calculate thermodynamic properties are investigated as well as dynamic correlation functions at finite temperatures for the one- dimensional spin-1/2 Heisenberg model. The first method is based on purification, which allows for the exact calculation of the operator trace. The second one is based on a sampling of the trace using minimally entangled states, whereas the third 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 the sampling method are applied to the two-dimensional J1-J2 model on the square lattice. Unfortunately, computing accurate results for very low temperatures is difficult due to an increase in the rejection probability, an issue related to the Monte Carlo sampling and known as critical slowing down.