De Nardis Jacopo, Gopalakrishnan Sarang, Vasseur Romain
Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université, 95302 Cergy-Pontoise Cedex, France.
Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev Lett. 2023 Nov 10;131(19):197102. doi: 10.1103/PhysRevLett.131.197102.
Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable spin chains have time-reversal and parity symmetries that are absent from the KPZ (Kardar-Parisi-Zhang) or stochastic Burgers equation, which force higher-order spin fluctuations to deviate from standard KPZ predictions. We put forward a nonlinear fluctuating hydrodynamic theory consisting of two coupled stochastic modes: the local spin magnetization and its effective velocity. Our theory fully explains the emergence of anomalous spin dynamics in isotropic chains: it predicts KPZ scaling for the spin structure factor but with a symmetric, quasi-Gaussian, distribution of spin fluctuations. We substantiate our results using matrix-product states calculations.
已知在可积各向同性自旋链中的有限温度自旋输运是超扩散的，其动态自旋关联据推测属于卡达尔 - 帕里西 - 张（KPZ）普适类。然而，可积自旋链具有时间反演和宇称对称性，而KPZ（卡达尔 - 帕里西 - 张）方程或随机伯格斯方程中不存在这些对称性，这使得高阶自旋涨落偏离标准KPZ预测。我们提出了一种由两个耦合随机模式组成的非线性涨落流体动力学理论：局部自旋磁化强度及其有效速度。我们的理论充分解释了各向同性链中反常自旋动力学的出现：它预测了自旋结构因子的KPZ标度，但自旋涨落具有对称的、准高斯分布。我们使用矩阵乘积态计算证实了我们的结果。
