| --- |
| license: mit |
| language: |
| - en |
| tags: |
| - physics |
| - cmt |
| pretty_name: CMT Benchmark |
| version: "2.0.0" |
| --- |
| # CMT-Benchmark |
|
|
| **CMT-Benchmark** is a specialized dataset of 50 original, research-level problems in Condensed Matter Theory (CMT) designed to evaluate the scientific reasoning, analytical, and computational capabilities of Large Language Models (LLMs). |
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|
| **Current version: `2.0.0`**. See [Version and Changelog](#version-and-changelog) for problem corrections and their impact on evaluation results. |
|
|
| ## Details |
| ### Authors |
| Haining Pan, James V. Roggeveen, Erez Berg, Juan Carrasquilla, Debanjan Chowdhury, Surya Ganguli, Federico Ghimenti, Juraj Hasik, Henry Hunt, Hong-Chen Jiang, Mason Kamb, Ying-Jer Kao, Ehsan Khatami, Michael J. Lawler, Di Luo, Titus Neupert, Xiaoliang Qi, Michael P. Brenner, Eun-Ah Kim |
|
|
| ### Description |
|
|
| Unlike traditional textbook-based benchmarks, CMT-Benchmark consists of bespoke problems authored by a panel of experts. The problems are designed to test if an AI can function as a scientific research assistant, requiring the synthesis of material knowledge with theoretical principles. The dataset covers seven major computational and theoretical methods including Hartree-Fock, Exact Diagonalization, and Quantum Monte Carlo. |
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|
| * **Funded by:** NSF (Awards 2433348, OAC-2118310, DMR-2237522), US-ONR, Swiss National Science Foundation, NTT Research, and the U.S. Department of Energy. |
| * **Language:** English. |
|
|
| ### Sources |
|
|
| * **Dataset:** [CMTBenchmark/cmt_benchmark](https://huggingface.co/datasets/CMTBenchmark/cmt_benchmark). The anonymous pre-release snapshot linked from the paper, [AnonBenchmark322/benchmark_data](https://huggingface.co/datasets/AnonBenchmark322/benchmark_data), is superseded by this repository and is no longer maintained (see [Changelog](#changelog)). |
| * **Evaluation Code:** [GitHub Repository](https://github.com/JamesRoggeveen/cmt_benchmark_data) |
| * **Paper:** [CMT-BENCHMARK: A BENCHMARK FOR CONDENSED MATTER THEORY BUILT BY EXPERT RESEARCHERS](https://arxiv.org/abs/2510.05228). |
|
|
| ## Structure |
|
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| The dataset contains 50 problems categorized by theoretical/computational methods: |
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|
| * **Exact Diagonalization (ED):** 16% (8 problems). |
| * **Statistical Mechanics (SM):** 12% (6 problems). |
| * **Quantum Monte Carlo (QMC):** 12% (6 problems). |
| * **Hartree-Fock (HF):** 10% (5 problems). |
| * **DMRG:** 8% (4 problems). |
| * **PEPS:** 6% (3 problems). |
| * **Variational Monte Carlo (VMC):** 4% (2 problems). |
| * **Other:** 32% (16 problems). |
|
|
| ## Creation |
| Problems were authored in a collaborative Google Sheet environment using a custom-built extension. Authors iteratively refined problems to identify gaps in LLM reasoning. |
| * **Technical Note on Infrastructure**: The custom Google Sheet integration and the LaTeX-to-Sympy parsing infrastructure used for automated grading are described in further detail in [Roggeveen et al. (2025)]( |
| https://doi.org/10.48550/arXiv.2505.11774). |
|
|
| ## Version and Changelog |
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| Report the dataset version with benchmark results. Each dataset update receives a new version and an entry below identifying the affected problems and corrections. |
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| ### Changelog |
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| Problems are identified by their `index` field in `cmt_data.jsonl`. |
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| #### v2.0.0 (2026-10-22) |
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| Fixes errors in 10 problems after expert review; no problems were added or removed. Seven reference answers changed. Re-evaluate earlier results on this version before comparing scores. ([Data corrections](https://huggingface.co/datasets/CMTBenchmark/cmt_benchmark/commit/5c33139a1420c76ac006ef87251730e6608ebf48)) |
|
|
| | Index | Type | Field(s) | Change | |
| | --- | --- | --- | --- | |
| | 2 | HF | prompt, solution | Brillouin-zone corners corrected from the `k_y` axis to the `k_x` axis to match the reference coordinates; one coordinate re-rounded (`2.41` → `2.42`). | |
| | 6 | VMC | solution | `a;b;d` → `a;b;d;e`: option (e) is equivalent to (d). | |
| | 8 | QMC | solution | `b;f;i` → `b;i`: the zero-temperature transition is 3D XY, not 3D Ising. | |
| | 9 | QMC | parameters | Added missing option `e` (`a;b;c;d` → `a;b;c;d;e`) so the grader can parse it. | |
| | 11 | DMRG | solution | Degeneracy `2^{N/2-1}` → `2^{N/2}`: fermion-parity superselection does not apply to this spin system. Central charge `c=1/2` unchanged. | |
| | 31 | Other | solution | `a;c` → `a`: statement (c) applies only to the connected correlator. | |
| | 36 | PEPS | prompt, solution | Removed stray `(g)` label; answer `g` → `b;c;d`, using the required semicolon separator. | |
| | 39 | Other | solution | Energy gap `2t_1(t_1/t_2)^n` → `2\frac{t_2^2-t_1^2}{t_2}(t_1/t_2)^n`: restored the edge-state normalization factor, verified by exact diagonalization. | |
| | 40 | Other | prompt | Option (d): `t_1(t_2/t_1)^{N_u}` → `t_1(t_1/t_2)^{N_u}`. Reference answer unchanged. | |
| | 42 | SM | prompt | Dimensionless ratio: `\rho \equiv \gamma/(m\tau)` → `\rho \equiv \gamma\tau/m`. Reference answer unchanged. | |
|
|
| #### v1.0.1 (2026-07-01) |
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| Clarifies two Hartree-Fock prompts. All 50 problems are retained; reference answers and grading parameters are unchanged. ([Data changes](https://huggingface.co/datasets/CMTBenchmark/cmt_benchmark/commit/32cf7268666a96094ec34724b96b482b3b175b90)) |
|
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| | Index | Type | Field(s) | Change | |
| | --- | --- | --- | --- | |
| | 0 | HF | prompt | Clarified particle density: "half-filling per site" → "half-particle per site". | |
| | 2 | HF | prompt | Removed "original" from "six original Brillouin zone corners". | |
|
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| #### v1.0.0 (2026-02-20) |
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| First release under `CMTBenchmark`, containing 50 problems. ([Dataset commit](https://huggingface.co/datasets/CMTBenchmark/cmt_benchmark/commit/f87948d421cc4f29b0333a91c0e3ae5dc5115bce)) |
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| Compared with the [anonymous pre-release snapshot](https://huggingface.co/datasets/AnonBenchmark322/benchmark_data) used in the paper (last updated 2025-09-25), problem 12 (DMRG) has one answer correction: `c;e` → `c`, because the prompt offers only choices (a) through (d). |
|
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| ## Model Performance Summary |
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| The following table summarizes the Overall Pass@1 rates (%) as reported in the paper. These numbers were obtained on the pre-release version of the dataset that preceded v1.0.0 (see [Changelog](#changelog)). |
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| | Model | Overall | |
| | --- | --- | |
| | GPT-4o | 2.0 | |
| | GPT-4.1 | 4.0 | |
| | GPT-5 | 30.0 | |
| | GPT-5-mini | 24.0 | |
| | GPT-5-nano | 14.0 | |
| | GPT-o3 | 26.0 | |
| | GPT-o4-mini | 18.0 | |
| | Gemini 2.0 Flash | 10.0 | |
| | Gemini 2.5 Flash | 4.0 | |
| | Gemini 2.5 Pro | 14.0 | |
| | Claude 3.7 Sonnet | 6.0 | |
| | Claude 4.1 Sonnet | 2.0 | |
| | Claude 4.0 Sonnet | 6.0 | |
| | Claude 4.1 Opus | 8.0 | |
| | Claude 4.0 Opus | 10.0 | |
| | DeepSeek v3 | 4.0 | |
| | LLaMA Maverick | 12.0 | |
|
|
| ## Citation |
|
|
| **BibTeX:** |
|
|
| ```bibtex |
| @misc{https://doi.org/10.48550/arxiv.2510.05228, |
| doi = {10.48550/ARXIV.2510.05228}, |
| url = {https://arxiv.org/abs/2510.05228}, |
| author = {Pan, Haining and Roggeveen, James V. and Berg, Erez and Carrasquilla, Juan and Chowdhury, Debanjan and Ganguli, Surya and Ghimenti, Federico and Hasik, Juraj and Hunt, Henry and Jiang, Hong-Chen and Kamb, Mason and Kao, Ying-Jer and Khatami, Ehsan and Lawler, Michael J. and Luo, Di and Neupert, Titus and Qi, Xiaoliang and Brenner, Michael P. and Kim, Eun-Ah}, |
| keywords = {Machine Learning (cs.LG), Artificial Intelligence (cs.AI), FOS: Computer and information sciences, FOS: Computer and information sciences}, |
| title = {CMT-Benchmark: A Benchmark for Condensed Matter Theory Built by Expert Researchers}, |
| publisher = {arXiv}, |
| year = {2025}, |
| copyright = {Creative Commons Zero v1.0 Universal} |
| } |
| ``` |
|
|
| ## Response to the Epoch AI review |
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| *Posted 2026-10-23 by the CMT-Benchmark authors, in reply to [Epoch AI's review of v1.0.0](https://epoch.ai/benchmarks/cmt-benchmark/review).* |
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|
| 1. **We had already found and fixed the real errors.** We were aware of problems in the original release before this review. We identified 10 of them ourselves, and the corrections are merged into this dataset as v2.0.0 (see the changelog above). The corrected problems are indices 2, 6, 8, 9, 11, 31, 36, 39, 40, and 42. That includes problem 31, the example the review shows. An earlier update (v1.0.1) had already revised problems 0 and 2. The Epoch review evaluates v1.0.0; results should be cited against the current version. |
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| 2. **We do not accept that 30 of the 50 problems are erroneous.** That figure comes from Ansari et al. (2026), who, as the review notes, graded with an LLM judge. In our reading, most of the items they flag are not errors. They are conventions standard in the relevant subfield that we deliberately left unstated. We wrote the problems as one would pose them to a graduate student or researcher in that area. Knowing those conventions is part of the expertise the benchmark is meant to test. An LLM-based audit will flag every unstated convention as a "missing assumption," but an unstated convention is not a scoring defect. Rewriting the problems to spell out every convention also makes them easier. So higher scores on the "repaired" set do not, by themselves, show that the original problems were graded wrongly. |
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| 3. **The grading code is public.** The official evaluation and parsing code is available at https://github.com/JamesRoggeveen/cmt_benchmark_data. Results on the benchmark should be computed with that scorer, not with an LLM judge. |
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| 4. **We are going through the remaining items flagged by Ansari et al.,** one problem at a time, with expert judgment. Where we agree that a problem is wrong or genuinely ambiguous, we will correct it in a versioned release with a changelog. |
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| We welcome careful outside scrutiny of the benchmark and would be glad to have Epoch review the corrected version. |
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|
| — Eun-Ah Kim, on behalf of the CMT-Benchmark authors |
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|
