Automating Hartree-Fock mean-field theory for condensed matter physics

Large language models (LLMs) have shown notable capabilities in handling complex tasks across a range of disciplines, including mathematical and scientific reasoning. In this work, we examine the ability of LLMs to perform analytical calculations commonly found in theoretical physics research. Our focus is on the Hartree-Fock method, a standard approximation technique in quantum physics, which involves deriving the approximate Hamiltonian and solving the self-consistency equations through multi-step calculations.

We designed structured prompt templates to guide LLMs in breaking down these calculations into manageable steps, with placeholders for problem-specific information. Using GPT-4 as a case study, we evaluated its performance on 15 research papers published over the past decade. The results indicate that GPT-4, with corrections to intermediate steps, correctly derives the Hartree-Fock Hamiltonian in 13 cases and makes minor errors in 2 cases. Across all examples, the model achieves an average score of 87.5 (out of 100) on individual calculation steps, demonstrating proficiency comparable to graduate-level work in quantum condensed matter theory.

Additionally, we explored the use of LLMs to streamline two key challenges: (i) extracting information from research papers to populate templates and (ii) automating the scoring of intermediate steps. The model showed satisfactory results in both tasks. These findings suggest that LLMs can assist in carrying out specific theoretical physics calculations with structured guidance.

Beyond analytical calculations, we will also demonstrate how carefully designed prompts using the latest LLMs can generate functional code, providing a potential framework for integrating coding tasks into research workflows.