Quantum Transport in Interacting Spin Chains: Exact Derivation of the GUE Tracy-Widom Distribution
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912171662770176 |
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| author | Fujimoto, Kazuya Sasamoto, Tomohiro |
| author_facet | Fujimoto, Kazuya Sasamoto, Tomohiro |
| contents | We theoretically study quantum spin transport in a one-dimensional folded XXZ model with an alternating domain-wall initial state via the Bethe ansatz technique, exactly demonstrating that a probability distribution of finding a left-most up-spin with an appropriate scaling variable converges to the Tracy-Widom distribution for the Gaussian unitary ensemble (GUE), which is a universal distribution for the largest eigenvalue of GUE under a soft-edge scaling limit. Our finding presented here offers a first exact derivation of the GUE Tracy-Widom distribution in the dynamics of the interacting quantum model not being mapped to a noninteracting fermion Hamiltonian via the Jordan-Wigner transformation. On the basis of the exact solution of the folded XXZ model and our numerical analysis of the XXZ model, we discuss a universal behavior for the probability of finding the left-most up-spin in the XXZ model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Transport in Interacting Spin Chains: Exact Derivation of the GUE Tracy-Widom Distribution Fujimoto, Kazuya Sasamoto, Tomohiro Statistical Mechanics Quantum Gases Quantum Physics We theoretically study quantum spin transport in a one-dimensional folded XXZ model with an alternating domain-wall initial state via the Bethe ansatz technique, exactly demonstrating that a probability distribution of finding a left-most up-spin with an appropriate scaling variable converges to the Tracy-Widom distribution for the Gaussian unitary ensemble (GUE), which is a universal distribution for the largest eigenvalue of GUE under a soft-edge scaling limit. Our finding presented here offers a first exact derivation of the GUE Tracy-Widom distribution in the dynamics of the interacting quantum model not being mapped to a noninteracting fermion Hamiltonian via the Jordan-Wigner transformation. On the basis of the exact solution of the folded XXZ model and our numerical analysis of the XXZ model, we discuss a universal behavior for the probability of finding the left-most up-spin in the XXZ model. |
| title | Quantum Transport in Interacting Spin Chains: Exact Derivation of the GUE Tracy-Widom Distribution |
| topic | Statistical Mechanics Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2412.20147 |