Distinct universality classes of diffusive transport from full counting statistics

Abstract

The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body 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 site-resolved 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 linear-response transport, but the higher moments go beyond. We present an analytic theory of the full counting statistics of spin transport in various integrable and non-integrable anisotropic one-dimensional spin models, including the XXZ spin chain. We find that spin transport, while diffusive on average, is governed by a distinct non-Gaussian 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 half-chains. We derive a closed-form expression for the probability distribution of the magnetization transfer, in terms of random walks on the half-line. We show that this distribution strongly violates the large-deviation 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.

11pp., 7 figures

References in corpus (12)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Probing many-body dynamics on a 51-atom quantum simulator
• The large deviation approach to statistical mechanics
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
• Ballistic spin transport in a periodically driven integrable quantum system
• Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics
• Kardar-Parisi-Zhang universality from soft gauge modes
• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Full counting statistics in the spin-1/2 Heisenberg XXZ chain
• Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems
• A Yang-Baxter integrable cellular automaton with a four site update rule

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