Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems

IF 14.3 1区物理与天体物理 Q1 PHYSICS, CONDENSED MATTER

Annual Review of Condensed Matter Physics Pub Date : 2023-11-21 DOI:10.1146/annurev-conmatphys-032922-110710

Sarang Gopalakrishnan, Romain Vasseur

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Abstract

The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is subballistic at any nonzero temperature: An initially localized spin fluctuation spreads in time t to a width t2/3. This exponent as well as the functional form of the dynamical spin correlation function suggest that spin transport is in the Kardar–Parisi–Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 15 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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近可积系统中非abel对称的超扩散

海森堡自旋链是一个正则可积模型。因此，它具有稳定的弹道传播准粒子，但自旋输运在任何非零温度下都是亚弹道的:最初的局部自旋涨落在时间t上传播到宽度t2/3。该指数以及动态自旋相关函数的函数形式表明，自旋输运属于kardar - paris - zhang (KPZ)普适类。然而，磁化的全计数统计与KPZ标度明显不相容。一个简单的双模流体力学描述，可以从微观原理推导出来，同时捕获相关函数的KPZ缩放和全计数统计的粗糙特征，但仍有待数值验证。这些结果推广到任何连续非阿贝尔对称下的可积自旋链不变量，并且对于尊重非阿贝尔对称的中等强可积破缺微扰具有惊人的鲁棒性。预计《凝聚态物理年度评论》第15卷的最终在线出版日期为2024年3月。修订后的估计数请参阅http://www.annualreviews.org/page/journal/pubdates。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annual Review of Condensed Matter Physics PHYSICS, CONDENSED MATTER-

CiteScore

47.40

自引率

0.90%

发文量

期刊介绍： Since its inception in 2010, the Annual Review of Condensed Matter Physics has been chronicling significant advancements in the field and its related subjects. By highlighting recent developments and offering critical evaluations, the journal actively contributes to the ongoing discourse in condensed matter physics. The latest volume of the journal has transitioned from gated access to open access, facilitated by Annual Reviews' Subscribe to Open initiative. Under this program, all articles are now published under a CC BY license, ensuring broader accessibility and dissemination of knowledge.