Statistical localization of <i>U</i>(1) lattice gauge theory in a Rydberg simulator

Nature Physics (2026)Cite this article Lattice gauge theories provide a framework for describing dynamical systems ranging from nuclei to materials. When they host concatenated conservation laws, their Hilbert space can fragment into subspaces labelled by non-local quantities—a phenomenon known as Hilbert space fragmentation. Although non-local conservation laws are expected not to hinder local thermalization, this assumption has been questioned by the idea of statistical localization, where motifs of microscopic configurations remain frozen owing to strong fragmentation. Here we observe experimental signatures of such behaviour in a constrained lattice gauge theory using a facilitated Rydberg-atom array, where atoms mediate the dynamics of charge clusters whose non-local net-charge patterns remain invariant. By reconstructing observables sampled over time, we probe the spatial distribution of conserved quantities. We find that strong Hilbert space fragmentation keeps these quantities locally distributed in typical quantum states, even though they are defined by non-local string-like operators. This establishes a setting for high-energy studies of cluster dynamics and low-energy investigations of strong zero modes that persist in infinite-temperature topological systems.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutThe data presented in this manuscript are available via Zenodo at https://doi.org/10.5281/zenodo.18012627 (ref. 77) and from the corresponding author upon reasonable request.Kogut, J. B. The lattice gauge theory approach to quantum chromodynamics. Rev. Mod. Phys. 55, 775 (1983).Article ADS Google Scholar Greensite, J. The confinement problem in lattice gauge theory. Prog. Part. Nucl. Phys. 51, 1–83 (2003).Article ADS Google Scholar Sachdev, S. Emergent gauge fields and the high-temperature superconductors. Philos. Trans. A 374, 20150248 (2016).ADS Google Scholar Scherg, S. et al. Observing non-ergodicity due to kinetic constraints in tilted Fermi–Hubbard chains. Nat. Commun. 12, 4490 (2021).Article ADS Google Scholar Kohlert, T. et al. Exploring the regime of fragmentation in strongly tilted Fermi–Hubbard chains. Phys. Rev. Lett. 130, 010201 (2023).Article ADS Google Scholar Adler, D. et al. Observation of Hilbert space fragmentation and fractonic excitations in 2D. Nature 636, 80 (2024).Article ADS Google Scholar Kim, K., Yang, F., Mølmer, K. & Ahn, J. Realization of an extremely anisotropic Heisenberg magnet in Rydberg atom arrays. Phys. Rev. X 14, 011025 (2024).

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J. Wee, A. Qu and J. You, as well as helpful discussions with M. M. Aliyu. W.W.H. is supported by the National Research Foundation (NRF), Singapore, through the NRF Fellowship NRF-NRFF15-2023-0008, and through the National Quantum Office, hosted in A*STAR, under its Centre for Quantum Technologies Funding Initiative (grant no. S24Q2d0009). N.K. acknowledges funding in part from the NSF STAQ Program (PHY-1818914). H.L. acknowledges support from the Alfred P. Sloan Foundation.Centre for Quantum Technologies and Department of Physics, National University of Singapore, Singapore, SingaporePrithvi Raj Datla, Luheng Zhao, Wen Wei Ho & Huanqian LohDepartment of Physics, Stanford University, Stanford, CA, USAPrithvi Raj DatlaDuke Quantum Center, Duke University, Durham, NC, USALuheng Zhao, Natalie Klco & Huanqian LohDepartment of Electrical and Computer Engineering, Duke University, Durham, NC, USALuheng Zhao & Huanqian LohDepartment of Physics, Duke University, Durham, NC, USANatalie Klco & Huanqian LohSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarP.R.D. and L.Z. ran the experiments and developed the theory simulations. W.W.H. and N.K. guided the theory work. H.L. supervised the project. All authors discussed the results and contributed to the manuscript.Correspondence to Huanqian Loh.The authors declare no competing interests.Nature Physics thanks Aaron Young and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.a, The atomic chain of ground and Rydberg atoms is first mapped to b, a chain of electric field strings on the bonds and charge clusters on the sites. Internal states of the atoms (ground or Rydberg) are mapped directly to electric field variables on the bonds, where right-facing strings alternate in correspondence between ground and Rydberg state atoms on odd and even bonds (vice versa for left-facing strings). c, Another mapping is performed to finally arrive at a spin representation. On odd sites, spin down (spin up) corresponds to a negative charge (vacua), whereas on even sites, spin down (spin up) corresponds to a vacua (positive charge). d, Tracing out the bond degrees of freedom leads to constrained spin dynamics on the matter sites, where spin-exchange is allowed between adjacent sites, only if the surrounding two sites are both spin-up or spin-down.We plot time-averaged Z-microstate projections \({\overline{P}}_{k}\) evolving from an initial state within \({{\mathcal{K}}}_{11}\) (Extended Data Table 1). The two distributions appear similar, indicating only a minor localizing effect from the position disorder.The distributions are more spread out towards the right side of the chain. This is because state preparation infidelity, our main source of imperfection, is more likely to result in initializing a state with \({N}_{c}^{{\prime} } 5\) (since \({{\mathcal{F}}}_{g} > {{\mathcal{F}}}_{r}\)). States belonging to a symmetry sector with Nc < 5 would naturally have their conserved charges more spread out across the chain, resulting in the broadening of distributions. Error bars depict the standard error of the mean.Atoms may flip their spins only if both of their nearest neighbors are in the ground state and exactly one of their next-nearest neighbors is in the Rydberg state. Schematically, these spin-flip conditions apply to atoms that 1. are not enveloped within the blockade radius of one of its next-nearest neighbors and 2. simultaneously intersect the facilitation shell of the other next-nearest neighbor. These conditions are realized by setting the global detuning to be the van der Waals interaction between two Rydberg atoms that are next-nearest neighbors, \(\varDelta\) = V1.a, Autocorrelators and b, microstate distributions are compared between the ideal case of V2 = 0 and the experimentally relevant case of V2 = 0.1Ω through numerical simulations.a, The number of Krylov fragments, NKrylov, scales exponentially as 1.22N. b, The size of the largest fragment Dmax as a fraction of the total Hilbert space dimension Dtotal vanishes for large N, indicating strong fragmentation. c, The fraction of fragments that are frozen (dimension one) approaches a finite value close to 1/3.a, Experimentally measured SLIOM distibutions, generated by temporal ensembles starting from Ωti = 0.56 and ending at Ωtf = 3 (open triangles), 4 (crosses), 5.6 (open circles). The error bars here depict the standard error of the mean. b, Numerically simulated SLIOM distibutions, generated by temporal ensembles (Ωti = 0.56, Ωtf = 5.6) starting from two different initial states (open circles for \(\left|\psi \right\rangle =\left|rgggggrggrgggggr\right\rangle \in {{\mathcal{K}}}_{6}\) and crosses for \(\left|{\psi }^{{\prime} }\right\rangle =\left|rgggrgrggrgrgggr\right\rangle \in {{\mathcal{K}}}_{6}\)) and compared with the infinite-temperature distribution within \({{\mathcal{K}}}_{6}\) (open triangles).a, Full-width-half-maxima σ of the center SLIOM distributions over the system size N, evaluated for system sizes ranging from N = 90 to N = 450. The number of clusters in the largest symmetry sector does not necessarily increase with every increment in the system size, explaining the sawtooth feature in the plot that becomes less prominent for larger N. The fractional width is observed to scale with an exponent α = 0.49, in agreement with our results in the main text. b, A scaling collapse of center SLIOM distributions shows that their width indeed appears to scale as \(\sqrt{N}\). The site index i is plotted such that the center site on the chain of particles corresponds to i = 0. Each curve has a jagged feature between half-integer sites and integer sites, leading to separated Bell-shaped distributions.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsDatla, P.R., Zhao, L., Ho, W.W. et al. Statistical localization of U(1) lattice gauge theory in a Rydberg simulator. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03183-wDownload citationReceived: 22 May 2025Accepted: 14 January 2026Published: 18 February 2026Version of record: 18 February 2026DOI: https://doi.org/10.1038/s41567-026-03183-wAnyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative