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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2604.03977 |
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| _version_ | 1866913005710606336 |
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| author | Li, Tingfei Li, Shuanghong |
| author_facet | Li, Tingfei Li, Shuanghong |
| contents | Recently, studies have explored the statistics of matrix elements of local operators in the Lieb-Liniger model. It was found that the probability distribution function for off-diagonal matrix elements $\langle \boldsymbolμ|\mathcal{O}|\boldsymbolλ \rangle$ within the same macro-state is well described by the Fréchet distributions. This represents a significant development for the Eigenstate Thermalization Hypothesis (ETH). In this paper, we investigate a similar phenomenon in another solvable model: the disorder-free Sachdev-Ye-Kitaev (SYK) model. The Hamiltonian of this model consists of 4-body interactions of Majorana fermions. Unlike the conventional SYK model, the coupling strengths in this model are fixed to a constant, earning it the name ``disorder-free.'' We evaluate the matrix elements of operators constructed from products of $n$ Majorana fermions: $\mathcal{O} = χ_{a_1}χ_{a_2}\ldots χ_{a_n}$. For a general choice of indices and $n \geq 4$, we find that the statistics of the off-diagonal matrix elements are well-fitted by a generalized inverse Gaussian distribution rather than Fréchet distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03977 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Statistics of Matrix Elements of Operators in a Disorder-Free SYK model Li, Tingfei Li, Shuanghong Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics Recently, studies have explored the statistics of matrix elements of local operators in the Lieb-Liniger model. It was found that the probability distribution function for off-diagonal matrix elements $\langle \boldsymbolμ|\mathcal{O}|\boldsymbolλ \rangle$ within the same macro-state is well described by the Fréchet distributions. This represents a significant development for the Eigenstate Thermalization Hypothesis (ETH). In this paper, we investigate a similar phenomenon in another solvable model: the disorder-free Sachdev-Ye-Kitaev (SYK) model. The Hamiltonian of this model consists of 4-body interactions of Majorana fermions. Unlike the conventional SYK model, the coupling strengths in this model are fixed to a constant, earning it the name ``disorder-free.'' We evaluate the matrix elements of operators constructed from products of $n$ Majorana fermions: $\mathcal{O} = χ_{a_1}χ_{a_2}\ldots χ_{a_n}$. For a general choice of indices and $n \geq 4$, we find that the statistics of the off-diagonal matrix elements are well-fitted by a generalized inverse Gaussian distribution rather than Fréchet distributions. |
| title | Statistics of Matrix Elements of Operators in a Disorder-Free SYK model |
| topic | Statistical Mechanics High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2604.03977 |