An integrated neural wavefunction solver for spinful Fermi systems

TL;DR

This paper introduces a novel neural wavefunction solver combining Monte Carlo sampling and transformer models to efficiently find ground states of spinful Fermi systems with complex spin interactions.

Contribution

It develops an integrated approach using transformers and Monte Carlo sampling to handle spin and coordinate degrees of freedom in Fermi systems, enabling faster convergence and universal approximation.

Findings

Faster convergence to antiferromagnetic ground states with spin updates.

Transformer-based wavefunctions achieve universal approximation of spinful orbitals.

Validated on 2D electron gas, spin textures, and quantum antiferromagnets.

Abstract

We present an approach to solving the ground state of Fermi systems that contain spin or other discrete degrees of freedom in addition to continuous coordinates. The approach combines a Markov chain Monte Carlo sampling for energy estimation that we adapted to cover the extended configuration space with a transformer-based wavefunction to represent fermionic states. This sampling is necessary when the Hamiltonian contains explicit spin dependence and, for spin-independent Hamiltonians, we find that the inclusion of spin updates leads to faster convergence to an antiferromagnetic ground state. A transformer with both continuous position and discrete spin as inputs achieves universal approximation to spinful generalized orbitals. We validate the method on a range of two-dimensional material problems: a two-dimensional electron gas with Rashba spin-orbit coupling, a noncollinear spin texture, and a quantum antiferromagnet in a honeycomb moir\'e potential.