Anomalous Diffusion in Dipole- and Higher-Moment-Conserving Systems

Johannes Feldmeier, Pablo Sala, Giuseppe De Tomasi, Frank Pollmann, and Michael Knap
Phys. Rev. Lett. 125, 245303 – Published 10 December 2020
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Abstract

The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher-moment generalizations thereof, escape this scenario, displaying subdiffusive decay instead. Modeling the time evolution as cellular automata for specific cases of dipole- and quadrupole conservation, we numerically find distinct anomalous exponents of the late time relaxation. We explain these findings by analytically constructing a general hydrodynamic model that results in a series of exponents depending on the number of conserved moments, yielding an accurate description of the scaling form of charge correlation functions. We analyze the spatial profile of the correlations and discuss potential experimentally relevant signatures of higher-moment conservation.

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  • Received 7 April 2020
  • Accepted 10 November 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.245303

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Johannes Feldmeier1,2, Pablo Sala1,2, Giuseppe De Tomasi3, Frank Pollmann1,2, and Michael Knap1,2

  • 1Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
  • 2Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 München, Germany
  • 3T.C.M. Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom

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Issue

Vol. 125, Iss. 24 — 11 December 2020

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