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Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-1/2 model

Nils Niggemann1,2,3, Meghadeepa Adhikary4,5, Yannik Schaden-Thillmann2,3, and Johannes Reuther2,3

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Phys. Rev. B 113, 165118 – Published 10 April, 2026

DOI: https://doi.org/10.1103/b2q3-mgvf

Abstract

Classical U(1) fracton spin liquids feature an extensive ground state degeneracy and follow an effective description in terms of a tensor Gauss's law where charges, so-called fractons, have restricted mobility. Here we introduce a simple spin model that realizes such a state by straightforward discretization of the higher-rank gauge theory on a square lattice. The simplicity of this construction offers direct insights into the system's fundamental fractonic properties, such as real-space fracton configurations, height-field representation of the classical ground state manifold as well as properties of local and nonlocal fluctuations within the fracton-free subspace. By sampling classical Ising states from the extensive ground state manifold, we show that the effective tensor Gauss's law remains intact when explicitly enforcing the spin-1/2 length constraint, demonstrating the existence of a classical Ising fracton spin liquid. However, we observe that perturbative quantum effects are insufficient to efficiently tunnel between classical ground states, leading to severe Hilbert space fragmentation which obscures fractonic quantum behavior. Specifically, by simulating the spin-1/2 quantum model with Green's function Monte Carlo as a function of the Rokhsar-Kivelson potential, we find that the system supports either magnetic long-range order or a classical spin liquid. Our findings highlight the crucial role of Hilbert-space fragmentation in fractonic spin systems but also indicate ways to mitigate such effects via increasing the spin magnitude to S=1, investigated in a companion paper.

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Phys. Rev. B 113, 165118– Published 10 April, 2026
  • Received 29 August 2025
  • Accepted 23 February 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.

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