Related papers: Quantum Transport in Interacting Spin Chains: Exact Derivation of the GUE Tracy-Widom Distribution

Quantum Transport in Interacting Spin Chains: Exact Derivation of the GUE Tracy-Widom Distribution

URL: http://arxiv.org/abs/2412.20147v1
Date: Sat, 28 Dec 2024 13:15:12 GMT
Title: Quantum Transport in Interacting Spin Chains: Exact Derivation of the GUE Tracy-Widom Distribution
Authors: Kazuya Fujimoto, Tomohiro Sasamoto,
Abstract summary: We study quantum spin transport in a one-dimensional folded XXZ model with an alternating domain-wall initial state via the Bethe ansatz technique. 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.
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Abstract: 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.

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