Fermionic neural Gibbs states

2025-12-04

AI Summary

This work addresses the scalability challenge in simulating strongly correlated fermionic systems at finite temperatures—particularly in two and higher dimensions. To this end, we propose fNGS (fermionic Neural Gibbs State), a variational framework that synergistically integrates the thermofield double (TFD) state as the initial ansatz, neural-network quantum states (NNQS) for representation, and imaginary-time evolution. This is the first approach to jointly model TFD and NNQS within a unified variational scheme. fNGS overcomes dimensional limitations and achieves high-accuracy thermal-state simulation of the Fermi–Hubbard model across a broad temperature range, strong coupling regimes, and large doping levels. Numerical benchmarks demonstrate significantly lower energy errors compared to existing variational methods and stable convergence on system sizes far exceeding those accessible via exact diagonalization. The method exhibits exceptional robustness and scalability, establishing a new paradigm for investigating thermodynamic properties of strongly correlated fermionic systems.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Adversarial Agents

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Computational social science
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We introduce fermionic neural Gibbs states (fNGS), a variational framework for modeling finite-temperature properties of strongly interacting fermions. fNGS starts from a reference mean-field thermofield-double state and uses neural-network transformations together with imaginary-time evolution to systematically build strong correlations. Applied to the doped Fermi-Hubbard model, a minimal lattice model capturing essential features of strong electronic correlations, fNGS accurately reproduces thermal energies over a broad range of temperatures, interaction strengths, even at large dopings, for system sizes beyond the reach of exact methods. These results demonstrate a scalable route to studying finite-temperature properties of strongly correlated fermionic systems beyond one dimension with neural-network representations of quantum states.

Problem

• Modeling finite-temperature properties of strongly interacting fermions
• Building strong correlations via neural networks and imaginary-time evolution
• Studying doped Fermi-Hubbard model beyond exact methods reach

Innovation

• Neural network transformations build strong correlations
• Imaginary-time evolution systematically enhances reference state
• Scalable framework for finite-temperature fermionic systems