Nonlinear Fluctuating Hydrodynamics for Kardar-Parisi-Zhang Scaling in Isotropic Spin Chains
Nonlinear Fluctuating Hydrodynamics for Kardar-Parisi-Zhang Scaling in Isotropic Spin Chains
复制标题
各向同性自旋链中 Kardar-Parisi-Zhang 尺度的非线性脉动流体动力学
DOI：
10.1103/physrevlett.131.197102
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发表时间：
2023
影响因子：
8.6
通讯作者：
Vasseur, Romain
中科院分区：
文献类型：
--
作者：
De Nardis, Jacopo;Gopalakrishnan, Sarang;Vasseur, Romain
可积各向同性自旋链中的有限温度自旋输运是超扩散的，动力学自旋关联被推测属于Kardar-Parisi-Zhang(KPZ)普适性类。然而，可积自旋链具有KPZ(Kardar-Parisi-Zhang)或随机Burgers方程所不存在的时间反转和宇称对称性，这迫使高阶自旋涨落偏离标准的KPZ预测。提出了一个由局域自旋磁化强度及其有效速度两个耦合随机模组成的非线性涨落流体力学理论。我们的理论完全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，但具有对称的准高斯自旋涨落分布。我们使用矩阵乘积态计算来证实我们的结果。
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.