Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems
Year: 2023
Type: review
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.
Authors: Sarang Gopalakrishnan, Romain Vasseur
Institutions: Princeton University, University of Massachusetts Amherst
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Awards: G1855896081, QUANTUM CRITICALITY AND TOPOLOGY IN NON-EQUILIBRIUM SYSTEMS, G2754565410, QUANTUM CRITICALITY AND TOPOLOGY IN NON-EQUILIBRIUM SYSTEMS, G6320007276, CAREER: Quantum many-body physics beyond the Boltzmann paradigm: prethermalization, many-body localization, and their applications, G755419668
OpenAlex ID: W4388869563