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  • Open Access

Fractional diffusion without disorder in two dimensions

Nilotpal Chakraborty1,2,*, Markus Heyl3, and Roderich Moessner1

  • *Contact author: nc553@cam.ac.uk
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Phys. Rev. Research 8, 033118 – Published 28 July, 2026

DOI: https://doi.org/10.1103/nbfk-s77d

Abstract

We analyze how simple local constraints in two dimensions lead a defect to exhibit robust, nontransient, and tunable subdiffusion. We uncover a rich dynamical phenomenology realized in ice- and dimer-type models. On the microscopic scale, a single defect exhibits anomalously long retractions. Such retractions result in a form of dynamical caging and can be captured through an effective fractional diffusion equation. Mapping to a height field yields an effective random walk subject to an emergent (entropic) logarithmic potential, whose strength is tunable, related to the exponent of algebraic ground-state correlations. The defect's path, viewed as nonequilibrium growth process, yields a frontier of fractal dimension of 5/4, the value for a loop-erased random walk, rather than 4/3 for simple and self-avoiding random walks. Such frustration/constraint-induced subdiffusion is expected to be relevant to platforms, such as artificial spin ice and quantum simulators aiming to realize discrete link models and emergent gauge theories.

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Phys. Rev. Research 8, 033118– Published 28 July, 2026
  • Received 14 April 2025
  • Accepted 27 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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