arXiv subjects

Shinya Ae

Publications and source records attributed to Shinya Ae.

3 recordsLinked to original sources

arXiv2026

Long-range correlation and the spin conductivity in the XXZ chain from ballistic macroscopic fluctuation theory

Based on the ballistic macroscopic fluctuation theory, the integration of the spin correlation function (spin conductivity) is analyzed for the spin-1/2 XXZ chain in the critical regime. In the time when the magnetization of an infinite spin chain fluctuates from an initial state with a wavelength as long as the infinite length $N$, the equal-time two-point spin correlation function is scaled up to $O(1/N)$. In the state where the ballistic spin transport decays at high temperature $T$, the diffusive transport remains on a large scale. We show that the spin conductivity is proportional to $1/T$ in the limit $T\to\infty$ and its high temperature proportionality constant diverges in the case where one-quasiparticle magnetization is infinitely large. This analysis informs that the superdiffusive spin transport is driven by the $1/N$-scaled long-range spin correlation and sheds a light on the dynamic scaling in spin transport at the isotropic point.

cond-mat.stat-mech↗

arXiv2023

Infinite temperature spin dc conductivity of the spin-1/2 XXZ chain

Using the Bethe ansatz method and the TBA equations for the higher spin integrable XXZ chain, the regular zero frequency contribution to the spin current correlation (spin dc conductivity) is analyzed for the spin-1/2 XXZ chain with an anisotropy $0 \le \Delta <1$. In the high temperature limit, we write down the dressed scattering kernels by one quasi-particle bare energies, which allows the exact evaluation of the infinite temperature spin dc conductivity $\mathcal{L}$. We find that $\mathcal{L}$ is discontinuous at all rational numbers of the anisotropy parameter $p_0=\pi/\cos^{-1}\Delta$ in the region $p_0 \ge 2$ with the gap increasing larger than the second power of growing magnetization on one quasi-particle. The isotropic $\Delta=1$ point is exceptional. Close to this point, $\mathcal{L}$ slowly increases in proportion to the first power of the magnetization. On the other hand $\mathcal{L}$ is proportional to the second power of the magnetization when $p_0$ approaches irrational numbers.

cond-mat.stat-mech↗

arXiv2023

Spin Drude weight for the integrable XXZ chain with arbitrary spin

Using generalized hydrodynamics (GHD), we exactly evaluate the finite-temperature spin Drude weight at zero magnetic field for the integrable XXZ chain with arbitrary spin and easy-plane anisotropy. First, we construct the fusion hierarchy of the quantum transfer matrices ($T$-functions) and derive functional relations ($T$- and $Y$-systems) satisfied by the $T$-functions and certain combinations of them ($Y$-functions). Through analytical arguments, the $Y$-system is reduced to a set of non-linear integral equations, equivalent to the thermodynamic Bethe ansatz (TBA) equations. Then, employing GHD, we calculate the spin Drude weight at arbitrary finite temperatures. As a result, a characteristic fractal-like structure of the Drude weight is observed at arbitrary spin, similar to the spin-1/2 case. In our approach, the solutions to the TBA equations (i.e., the $Y$-functions) can be explicitly written in terms of the $T$-functions, thus allowing for a systematic calculation of the high-temperature limit of the Drude weight.

cond-mat.stat-mech↗