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Physical review. B./Physical review. B

Integrated neural wave-function solver for spinful Fermi systems

Alexander Avdoshkin, Max Geier, Liang Fu

Published Feb 25, 2026• 0 citations
Publisher
DOI
10.1103/9pwc-s37d

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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 moiré potential.
Solving a multivariable static Schr\"odinger equation for a quantum system, to produce multiple excited-state energy eigenvalues and wave functions, is one of the basic tasks in mathematical and computational physics. Here we propose a neural-network-based solver, which enables us to cover the high-dimensional variable space for this purpose. The efficiency of the solver is analyzed by examples aimed at demonstrating the concept and various aspects of the task: the simultaneous finding of multiple excited states of lowest energies, the computation of energy-degenerate states with orthogonalized wave functions, the scalability to handle a multivariable problem, and the self-consistent determination and automatic adjustment of the imbedded Monte Carlo procedure. The solver adheres to the computational techniques developed in machine learning and is vastly different from traditional numerical methods.