Distinct universality classes of diffusive transport from full counting statistics
Abstract
The hydrodynamic transport of local conserved densities furnishes an effective coarsegrained description of the dynamics of a manybody quantum system. However, the full quantum dynamics contains much more structure beyond the simplified hydrodynamic description. Here we show that systems with the same hydrodynamics can nevertheless belong to distinct dynamical universality classes, as revealed by new classes of experimental observables accessible in synthetic quantum systems, which can, for instance, measure simultaneous siteresolved snapshots of all of the particles in a system. Specifically, we study the full counting statistics of spin transport, whose first moment is related to linearresponse transport, but the higher moments go beyond. We present an analytic theory of the full counting statistics of spin transport in various integrable and nonintegrable anisotropic onedimensional spin models, including the XXZ spin chain. We find that spin transport, while diffusive on average, is governed by a distinct nonGaussian dynamical universality class in the models considered. We consider a setup in which the left and right half of the chain are initially created at different magnetization densities, and consider the probability distribution of the magnetization transferred between the two halfchains. We derive a closedform expression for the probability distribution of the magnetization transfer, in terms of random walks on the halfline. We show that this distribution strongly violates the largedeviation form expected for diffusive chaotic systems, and explain the physical origin of this violation. We discuss the crossovers that occur as the initial state is brought closer to global equilibrium. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays.
 Publication:

arXiv eprints
 Pub Date:
 March 2022
 DOI:
 10.48550/arXiv.2203.09526
 arXiv:
 arXiv:2203.09526
 Bibcode:
 2022arXiv220309526G
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Strongly Correlated Electrons;
 Quantum Physics
 EPrint:
 11pp., 7 figures