Average topological phase in a disordered Rydberg atom array

Nature Physics (2026)Cite this article Topological phases have been widely studied in quantum pure states, where exact symmetries protect them. Such symmetry-protected topological phases have been observed in a range of systems, from solid-state materials to synthetic quantum platforms. Recent theory predicts that average symmetry-protected topological phases can also emerge in mixed quantum states that arise in realistic settings with decoherence or disorder, but experiments have not yet established them. Here we report observations of a disorder-induced many-body interacting average symmetry-protected topological phase in an atom array. We introduce structural disorder by applying random offsets to the tweezer positions that define the lattice, which generates fluctuating long-range dipolar interactions between confined atoms. Spatially resolved atom–atom correlation functions for different dimer configurations characterize the resulting induced topological phase. We detect ground-state degeneracy across disordered configurations and compare it directly with the ordered case. Finally, by probing the quench dynamics of a highly excited state, we observe slower decay of edge spin magnetization than in the bulk, consistent with topologically protected edge modes in the disordered lattice.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 datasets generated and analysed during the current study are available via Figshare at https://doi.org/10.6084/m9.figshare.30752111 (ref. 77). Source data are provided with this paper.Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045 (2010).Article ADS Google Scholar Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011).Article ADS Google Scholar Haldane, F. D. M. Nonlinear field theory of large-spin heisenberg antiferromagnets: semiclassically quantized solitons of the one-dimensional easy-axis néel state. Phys. Rev. Lett. 50, 1153 (1983).Article ADS MathSciNet Google Scholar Chen, X., Gu, Z.-C. & Wen, X.-G. Classification of gapped symmetric phases in one-dimensional spin systems. Phys. Rev. B 83, 035107 (2011).Article ADS Google Scholar Schuch, N., Pérez-García, D. & Cirac, I. Classifying quantum phases using matrix product states and projected entangled pair states. Phys. Rev. B 84, 165139 (2011).Article ADS Google Scholar Pollmann, F., Turner, A. M., Berg, E. & Oshikawa, M. Entanglement spectrum of a topological phase in one dimension. Phys. Rev. B 81, 064439 (2010).Article ADS Google Scholar Chen, X., Gu, Z.-C., Liu, Z.-X. & Wen, X.-G. Symmetry-protected topological orders in interacting bosonic systems. Science 338, 1604 (2012).Article ADS MathSciNet Google Scholar Chen, X., Gu, Z.-C., Liu, Z.-X. & Wen, X.-G. Symmetry protected topological orders and the group cohomology of their symmetry group. Phys. Rev. B 87, 155114 (2013).Article ADS Google Scholar Senthil, T. Symmetry-protected topological phases of quantum matter. Annu. Rev. Condens. Matter Phys. 6, 299 (2015).Article ADS Google Scholar Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018).Article Google Scholar Ringel, Z., Kraus, Y. E. & Stern, A. Strong side of weak topological insulators. Phys. Rev. B 86, 045102 (2012).Article ADS Google Scholar Mong, R. S. K., Bardarson, J. H. & Moore, J. E. Quantum transport and two-parameter scaling at the surface of a weak topological insulator. Phys. Rev. Lett. 108, 076804 (2012).Article ADS Google Scholar Fu, L. & Kane, C. L. Topology, delocalization via average symmetry and the symplectic anderson transition. Phys. Rev. Lett. 109, 246605 (2012).Article ADS Google Scholar Fulga, I., Van Heck, B., Edge, J. & Akhmerov, A. Statistical topological insulators. Phys. Rev. B 89, 155424 (2014).Article ADS Google Scholar Wang, J.-H., Yang, Y.-B., Dai, N. & Xu, Y. Structural-disorder-induced second-order topological insulators in three dimensions. Phys. Rev. Lett. 126, 206404 (2021).Article ADS Google Scholar Ma, R. & Wang, C. Average symmetry-protected topological phases. Phys. Rev. X 13, 031016 (2023).

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Topological phase transitions and mixed state order in a Hubbard quantum simulator. Preprint at https://doi.org/10.48550/arXiv.2505.17009 (2025).Hauschild, J. & Pollmann, F. Efficient numerical simulations with tensor networks: Tensor Network Python (TeNPy). SciPost Phys. Lect. Notes https://doi.org/10.21468/SciPostPhysLectNotes.5 (2018).Yue, Z. et al. Data of observation of a disorder-induced many-body interacting average symmetry-protected topological phase. Figshare https://doi.org/10.6084/m9.figshare.30752111 (2026).Download referencesWe acknowledge invaluable help and enlightening discussions with C. Chen, S. Huang, X. Chen, and S. Shen. Density matrix renormalization group (DMRG) calculations were performed using the TeNPy tensor network library76. We also acknowledge the support by the Center of High Performance Computing, Tsinghua University. L.Y. is supported by NSFC (grants 92265205 and 92565306). M.K.T. is supported by NSFC (grants 12234012 and W2431002). Y.-F.M., K.L. and Y.X. are supported by NSFC (grants 12474265 and 11974201) and Quantum Science and Technology-National Science and Technology Major Project (grant 2021ZD0301604). This work is also supported by Quantum Science and Technology-National Science and Technology Major Project (grant 2021ZD0302104).These authors contributed equally: Zongpei Yue, Yu-Feng Mao, Xinhui Liang.State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, ChinaZongpei Yue, Xinhui Liang, Zhen-Xing Hua, Peiyun Ge, Yu-Xin Chao, Chen Jia, Meng Khoon Tey & Li YouCenter for Quantum Information, IIIS, Tsinghua University, Beijing, ChinaYu-Feng Mao, Kai Li & Yong XuBeijing Academy of Quantum Information Sciences, Beijing, ChinaXinhui Liang & Li YouFrontier Science Center for Quantum Information, Beijing, ChinaZhen-Xing Hua, Peiyun Ge, Yu-Xin Chao, Chen Jia, Meng Khoon Tey & Li YouRIKEN Center for Emergent Matter Science, Wako, JapanKai LiHefei National Laboratory, Hefei, ChinaMeng Khoon Tey, Yong Xu & Li YouSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarZ.Y., Y.-F.M. and X.L. contributed equally to this work. Z.Y., Z.-X.H. and C.J. performed the experiments while also collecting and processing the data. Y.-F.M. and K.L. conducted numerical simulations and carried out theoretical analysis under the supervision of Y.X. Z.Y., X.L., Y.-X.C. and Z.-X.H. built the experimental platform led by M.K.T. Z.Y., Y.-F.M., M.K.T., Y.X. and L.Y. wrote the manuscript. M.K.T., Y.X. and L.Y. supervised the work. All authors contributed to the data analysis and progression of the project.Correspondence to Meng Khoon Tey, Yong Xu or Li You.The authors declare no competing interests.Nature Physics thanks the 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.Supplementary Information, sections 1–3, Supplementary Figs. 1–6, Supplementary Table 1 and Supplementary References.Statistical source data.Statistical source data.Statistical source data.Statistical source data.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 permissionsYue, Z., Mao, YF., Liang, X. et al. Average topological phase in a disordered Rydberg atom array. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03271-xDownload citationReceived: 02 July 2025Accepted: 26 March 2026Published: 20 April 2026Version of record: 20 April 2026DOI: https://doi.org/10.1038/s41567-026-03271-xAnyone 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