Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems

Gopalakrishnan, Sarang; Vasseur, Romain

doi:10.1146/annurev-conmatphys-032922-110710

Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems

Journal Article · Mon Nov 20 23:00:00 EST 2023 · Annual Review of Condensed Matter Physics

DOI:https://doi.org/10.1146/annurev-conmatphys-032922-110710· OSTI ID:2376128

Gopalakrishnan, Sarang ^[1]; Vasseur, Romain ^[2]

Princeton University, NJ (United States); UMass Amherst
University of Massachusetts, Amherst, MA (United States)

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 t^2/3. 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.

View Accepted Manuscript (DOE)

Research Organization:: University of Massachusetts, Amherst, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE); National Science Foundation (NSF)

Grant/Contract Number:: SC0023999

OSTI ID:: 2376128

Journal Information:: Annual Review of Condensed Matter Physics, Journal Name: Annual Review of Condensed Matter Physics Journal Issue: 1 Vol. 15; ISSN 1947-5454

Publisher:: Annual ReviewsCopyright Statement

Country of Publication:: United States

Language:: English

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