# Quantum Many-Body Physics Calculations with Large Language Models

arXiv: https://arxiv.org/abs/2403.03154 · HTML: https://mlsanity.com/paper/2403.03154/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 5 Mar 2024.

## Builds on (most cited first, 23 of 23)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [HuggingGPT: Solving AI Tasks with ChatGPT and its Friends in Hugging Face](https://mlsanity.com/paper/2303.17580/) (2023)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [Capabilities of GPT-4 on Medical Challenge Problems](https://mlsanity.com/paper/2303.13375/) (2023)
- [Chameleon: Plug-and-Play Compositional Reasoning with Large Language Models](https://mlsanity.com/paper/2304.09842/) (2023)
- [PaperQA: Retrieval-Augmented Generative Agent for Scientific Research](https://mlsanity.com/paper/2312.07559/) (2023)
- [Emergent autonomous scientific research capabilities of large language models](https://mlsanity.com/paper/2304.05332/) (2023)
- [The Impact of Large Language Models on Scientific Discovery: a Preliminary Study using GPT-4](https://mlsanity.com/paper/2311.07361/) (2023)
- [AI-assisted coding: Experiments with GPT-4](https://mlsanity.com/paper/2304.13187/) (2023)
- [Examining the Potential and Pitfalls of ChatGPT in Science and Engineering Problem-Solving](https://mlsanity.com/paper/2310.08773/) (2023)

## Built on by (most cited first, 17 of 17)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [Theoretical Physics Benchmark (TPBench) -- a Dataset and Study of AI Reasoning Capabilities in Theoretical Physics](https://mlsanity.com/paper/2502.15815/) (2025)
- [CURIE: Evaluating LLMs On Multitask Scientific Long Context Understanding and Reasoning](https://mlsanity.com/paper/2503.13517/) (2025)
- [When AI Co-Scientists Fail: SPOT-a Benchmark for Automated Verification of Scientific Research](https://mlsanity.com/paper/2505.11855/) (2025)
- [FEABench: Evaluating Language Models on Multiphysics Reasoning Ability](https://mlsanity.com/paper/2504.06260/) (2025)
- [QAgent: An LLM-based Multi-Agent System for Autonomous OpenQASM programming](https://mlsanity.com/paper/2508.20134/) (2025)
- [Automating High Energy Physics Data Analysis with LLM-Powered Agents](https://mlsanity.com/paper/2512.07785/) (2025)
- [Can Theoretical Physics Research Benefit from Language Agents?](https://mlsanity.com/paper/2506.06214/) (2025)
- [Agentic Exploration of Physics Models](https://mlsanity.com/paper/2509.24978/) (2025)
- [Advancing AI-Scientist Understanding: Multi-Agent LLMs with Interpretable Physics Reasoning](https://mlsanity.com/paper/2504.01911/) (2025)
- [CMT-Benchmark: A Benchmark for Condensed Matter Theory Built by Expert Researchers](https://mlsanity.com/paper/2510.05228/) (2025)
- [Bethe Ansatz with a Large Language Model](https://mlsanity.com/paper/2603.29932/) (2026)
- [Grading the Unspoken: Evaluating Tacit Reasoning in Quantum Field Theory and String Theory with LLMs](https://mlsanity.com/paper/2604.14188/) (2026)
- [Scaling Particle Collision Data Analysis](https://mlsanity.com/paper/2412.00129/) (2024)
- [Attention to Order: Transformers Discover Phase Transitions via Learnability](https://mlsanity.com/paper/2510.07401/) (2025)
- [From Paper to Program: Specification-Guided Implementation of Quantum Many-Body Algorithms with Large Language Model](https://mlsanity.com/paper/2604.04089/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have demonstrated an unprecedented ability to perform complex tasks in multiple domains, including mathematical and scientific reasoning. We demonstrate that with carefully designed prompts, LLMs can accurately carry out key calculations in research papers in theoretical physics. We focus on a broadly used approximation method in quantum physics: the Hartree-Fock method, requiring an analytic multi-step calculation deriving approximate Hamiltonian and corresponding self-consistency equations. To carry out the calculations using LLMs, we design multi-step prompt templates that break down the analytic calculation into standardized steps with placeholders for problem-specific information. We evaluate GPT-4's performance in executing the calculation for 15 research papers from the past decade, demonstrating that, with correction of intermediate steps, it can correctly derive the final Hartree-Fock Hamiltonian in 13 cases and makes minor errors in 2 cases. Aggregating across all research papers, we find an average score of 87.5 (out of 100) on the execution of individual calculation steps. Overall, the requisite skill for doing these calculations is at the graduate level in quantum condensed matter theory. We further use LLMs to mitigate the two primary bottlenecks in this evaluation process: (i) extracting information from papers to fill in templates and (ii) automatic scoring of the calculation steps, demonstrating good results in both cases. The strong performance is the first step for developing algorithms that automatically explore theoretical hypotheses at an unprecedented scale.