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

[2508.06606] Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Strongly Correlated Electrons arXiv:2508.06606 (cond-mat) [Submitted on 8 Aug 2025 ( v1 ), last revised 11 Apr 2026 (this version, v2)] Title: Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model Authors: Nils Niggemann , Meghadeepa Adhikary , Yannik Schaden-Thillmann , Johannes Reuther View a PDF of the paper titled Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model, by Nils Niggemann and 2 other authors View PDF HTML (experimental) Abstract: Classical U(1) fracton spin liquids feature an extensive ground state degeneracy and follow an effective description in terms of a tensor Gauss' 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 non-local fluctuations within the fracton-free subspace. By sampling classical Ising states from the extensive ground state manifold, we show that the effective tensor Gauss' 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 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. Comments: 11 pages (3 figs)+ 8 appendix (3 figs) Subjects: Strongly Correlated Electrons (cond-mat.str-el) ; Quantum Gases (cond-mat.quant-gas) Cite as: arXiv:2508.06606 [cond-mat.str-el] (or arXiv:2508.06606v2 [cond-mat.str-el] for this version) https://doi.org/10.48550/arXiv.2508.06606 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. B 113, 165118, 2026 Related DOI : https://doi.org/10.1103/b2q3-mgvf Focus to learn more DOI(s) linking to related resources Submission history From: Nils Niggemann [ view email ] [v1] Fri, 8 Aug 2025 18:00:02 UTC (1,323 KB) [v2] Sat, 11 Apr 2026 16:04:53 UTC (1,374 KB) Full-text links: Access Paper: View a PDF of the paper titled Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model, by Nils Niggemann and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.str-el < prev | next > new | recent | 2025-08 Change to browse by: cond-mat cond-mat.quant-gas References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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