Challenges for simulating quantum spin dynamics in two dimensions by neural network quantum states

Neural-network quantum states are a versatile ansatz for the representation of quantum states and in particular have shown promise for highly entangled ground states in two-dimensional spin systems. They have also been successfully applied to simulating dynamics by propagation with time-dependent variational Monte Carlo (t-VMC) [1-4], which is a stochastic version of the time-dependent variational principle (TDVP). However, there are a number of open challenges on the way to achieving stable time propagation for a wider range of systems and excitations [2,5,6].

In this work, we employ both t-VMC and deterministic TDVP-based propagation to spin-1/2 Heisenberg systems and take a closer look at various sources of error which can affect the stability and accuracy of the resulting dynamics. In particular, we analyze the influence of network expressiveness, the TDVP equation of motion and its numerical solution, and stochastic effects originating from VMC sampling.

[1] Carleo, Troyer, Science 355, 602 (2017)
[2] Schmitt, Heyl, PRL 125, 100503 (2020)
[3] Fabiani, Mentink, SciPost Phys 7, 004 (2019)
[4] Fabiani, Mentink, arXiv:1912.10845
[5] Czischek et al., PRB 98, 024311 (2018)
[6] López Gutiérrez, Mendl, arXiv:1912.08831