Distinct universality classes of diffusive transport from full counting statistics

Journal Article · Fri Jan 12 00:00:00 EST 2024 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.109.024417· OSTI ID:2283151

Gopalakrishnan, Sarang ^[1]; Morningstar, Alan ^[2]; Vasseur, Romain ^[3]; Khemani, Vedika ^[4]

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1. Pennsylvania State University, University Park, PA (United States); UMass Amherst
2. Princeton University, NJ (United States)
3. University of Massachusetts, Amherst, MA (United States)
4. Stanford University, CA (United States)

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 nonintegrable 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. Here, 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.

• Research Organization: University of Massachusetts, Amherst, MA (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)
• Grant/Contract Number: SC0021111; SC0023999
• OSTI ID: 2283151
• Alternate ID(s): OSTI ID: 2473569
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 2 Vol. 109; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Anomalous diffusion
Full counting statistics
Integrable systems