Discovering Quantum Ground States with Machine Learning Inspired Variational Approaches

Determining properties of strongly correlated electron systems using variational wave functions has a long history in physics. However, to date, few approaches have yet to demonstrate consistently a predictive power that can lead to physical results or insights beyond the reach of existing capabilities.The development of machine learning inspired tools and approaches has generated great interest to develop a more black-box approach, including the automatic detection of ground state order.

We present two studies, one on the lattice and the other in the continuum, to “discover” ground state order via variational optimization. On the lattice, we propose a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte Carlo and modern variational optimization techniques including automatic differentiation [1]. Then in a continuum system of the uniform two-dimensional electron gas (2DEG), we use a single variational ansatz of general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description of the phase diagram [2]. We show the performance of the two methods and their ability of systematic improvement and potential for symmetry restoration, including the discovery of novel physics in the 2DEG. We will also see how the corresponding ground state order manifests within the ansatz itself.

[1] Levy, Morales, Zhang, Phys. Rev. Research 6, 013237 (2024)

[2] Smith, Chen, Levy, Yang, Morales, Zhang, Phys. Rev. Lett. (2024) arxiv:2405.19397