Intertwined orders in a quantum-entangled metal

Nature Materials (2026)Cite this article Entanglement underpins quantum computing and information processing, yet its quantitative characterization in correlated materials remains an outstanding challenge. Here we report a highly entangled electronic phase near a quantum metal–insulator transition identified by resonant inelastic X-ray scattering interferometry. Entanglement extending across atomic sites generates distinct interference patterns that are accurately captured by theoretical modelling, enabling quantitative reconstruction of the entanglement spectrum and microscopic resolution of the underlying quantum states. In the pyrochlore iridate Nd2Ir2O7, pronounced quantum fluctuations of spin, orbital and charge persist within the long-range ‘all-in-all-out’ antiferromagnetic order. The observed entanglement signatures indicate the coexistence of multiple symmetry-breaking orders, supported by complementary Raman spectroscopy investigations. A two-magnon bound state appears below the lowest single-magnon excitation energy, which together with split phonon modes indicates a cubic symmetry breaking of magnetic origin coexisting with the all-in-all-out order. These findings establish a quantitative framework linking quantum entanglement to emergent unconventional orders.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 checkoutAll data are available in the manuscript or the Supplementary Information.Aspect, A., Dalibard, J. & Roger, G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982).Article Google Scholar Sachdev, S. Quantum phase transitions. Phys. World 12, 33 (1999).Article CAS Google Scholar Chubukov, A. V., Sachdev, S. & Senthil, T. Quantum phase transitions in frustrated quantum antiferromagnets. Nucl. Phys. B 426, 601–643 (1994).Laurell, P., Scheie, A., Dagotto, E. & Tennant, D. A. Witnessing entanglement and quantum correlations in condensed matter: a review. Adv. Quantum Technol. 8, 2400196 (2024).Scheie, A. et al. Witnessing entanglement in quantum magnets using neutron scattering. Phys. Rev. B 103, 224434 (2021).Article CAS Google Scholar Hales, J. et al. Witnessing light-driven entanglement using time-resolved resonant inelastic X-ray scattering. Nat. Commun. 14, 3512 (2023).Article CAS PubMed PubMed Central Google Scholar Ren, T. et al. Witnessing quantum entanglement using resonant inelastic X-ray scattering. Preprint at https://doi.org/10.48550/arXiv.2404.05850 (2024).Yanagishima, D. & Maeno, Y. Metal–nonmetal changeover in pyrochlore iridates. J. Phys. Soc. Jpn 70, 2880–2883 (2001).Article CAS Google Scholar Ueda, K., Fujioka, J. & Tokura, Y. Variation of optical conductivity spectra in the course of bandwidth-controlled metal-insulator transitions in pyrochlore iridates. Phys. Rev. B 93, 245120 (2016).Article Google Scholar Tomiyasu, K. et al. Emergence of magnetic long-range order in frustrated pyrochlore Nd2Ir2O7 with metal–insulator transition. J. Phys. Soc. Jpn 81, 034709 (2012).Article Google Scholar Guo, H., Ritter, C. & Komarek, A. C. Direct determination of the spin structure of Nd2Ir2O7 by means of neutron diffraction. Phys. Rev. B 94, 161102 (2016).Article Google Scholar Sagayama, H. et al. Determination of long-range all-in-all-out ordering of Ir4+ moments in a pyrochlore iridate Eu2Ir2O7 by resonant x-ray diffraction. Phys. Rev. B 87, 100403 (2013).Article Google Scholar Disseler, S. M. Direct evidence for the all-in/all-out magnetic structure in the pyrochlore iridates from muon spin relaxation. Phys. Rev. B 89, 140413 (2014).Article Google Scholar Abrikosov, A. A. Calculation of critical indices for zero-gap semiconductors. Zh. Eksp. Teor. Fiz. 66, 1443–1460 (1974).

Google Scholar Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).Article Google Scholar Witczak-Krempa, W. & Kim, Y. B. Topological and magnetic phases of interacting electrons in the pyrochlore iridates. Phys. Rev. B 85, 045124 (2012).Article Google Scholar Moon, E.-G., Xu, C., Kim, Y. B. & Balents, L. Non-Fermi-liquid and topological states with strong spin-orbit coupling. Phys. Rev. Lett. 111, 206401 (2013).Article PubMed Google Scholar Savary, L., Moon, E.-G. & Balents, L. New type of quantum criticality in the pyrochlore iridates. Phys. Rev. X 4, 041027 (2014).CAS Google Scholar Goswami, P., Roy, B. & Das Sarma, S. Competing orders and topology in the global phase diagram of pyrochlore iridates. Phys. Rev. B 95, 085120 (2017).Article Google Scholar Boettcher, I. & Herbut, I. F. Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals. Phys. Rev. B 95, 075149 (2017).Article Google Scholar Szabó, A. L., Moessner, R. & Roy, B. Interacting spin- \(\frac{3}{2}\) fermions in a Luttinger semimetal: competing phases and their selection in the global phase diagram. Phys. Rev. B 103, 165139 (2021).Nakayama, M. et al. Slater to Mott crossover in the metal to insulator transition of Nd2Ir2O7. Phys. Rev. Lett. 117, 056403 (2016).Article CAS PubMed Google Scholar Donnerer, C. et al. All-in–all-out magnetic order and propagating spin waves in Sm2Ir2O7. Phys. Rev. Lett. 117, 037201 (2016).Article CAS PubMed Google Scholar Ueda, K. et al. Phonon anomalies in pyrochlore iridates studied by Raman spectroscopy. Phys. Rev. B 100, 115157 (2019).Article CAS Google Scholar Xu, Y. et al. Phonon spectrum of Pr2Zr2O7 and Pr2Ir2O7 as evidence of coupling of the lattice with electronic and magnetic degrees of freedom. Phys. Rev. B 105, 075137 (2022).Article CAS Google Scholar Xu, J. et al. Magnetic structure and crystal-field states of the pyrochlore antiferromagnet Nd2Zr2O7. Phys. Rev. B 92, 224430 (2015).Article Google Scholar Lee, E. K.-H., Bhattacharjee, S. & Kim, Y. B. Magnetic excitation spectra in pyrochlore iridates. Phys. Rev. B 87, 214416 (2013).Article Google Scholar Bethe, H. Zur theorie der metalle: I. Eigenwerte und eigenfunktionen der linearen atomkette. Z. Phys. 71, 205–226 (1931).Article CAS Google Scholar Hanus, J. Bound states in the Heisenberg ferromagnet. Phys. Rev. Lett. 11, 336–338 (1963).Article Google Scholar Wortis, M. Bound states of two spin waves in the Heisenberg ferromagnet. Phys. Rev. 132, 85–97 (1963).Article CAS Google Scholar Chubukov, A. V. Chiral, nematic, and dimer states in quantum spin chains. Phys. Rev. B 44, 4693–4696 (1991).Article CAS Google Scholar Shannon, N., Momoi, T. & Sindzingre, P. Nematic order in square lattice frustrated ferromagnets. Phys. Rev. Lett. 96, 027213 (2006).Article PubMed Google Scholar Zhitomirsky, M. E. & Tsunetsugu, H. Magnon pairing in quantum spin nematic. Europhys. Lett. 92, 37001 (2010).Article Google Scholar Pradhan, S., Patel, N. D. & Trivedi, N. Two-magnon bound states in the Kitaev model in a [111] field. Phys. Rev. B 101, 180401 (2020).Article CAS Google Scholar Sheng, J. et al. Bose–Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice. Nat. Mater. 24, 544–551 (2025).Kim, H. et al. Quantum spin nematic phase in a square-lattice iridate. Nature 625, 264–269 (2024).Article CAS PubMed Google Scholar Witczak-Krempa, W., Go, A. & Kim, Y. B. Pyrochlore electrons under pressure, heat, and field: shedding light on the iridates. Phys. Rev. B 87, 155101 (2013).Article Google Scholar Kobayashi, S., Bhattacharya, A., Timm, C. & Brydon, P. M. R. Bogoliubov Fermi surfaces from pairing of emergent \(j=\frac{3}{2}\) fermions on the pyrochlore lattice. Phys. Rev. B 105, 134507 (2022).Tian, Z. et al. Field-induced quantum metal–insulator transition in the pyrochlore iridate Nd2Ir2O7. Nat. Phys. 12, 134–138 (2016).Article CAS Google Scholar Berke, C., Michetti, P. & Timm, C. Stability of the Weyl-semimetal phase on the pyrochlore lattice. New J. Phys. 20, 043057 (2018).Article Google Scholar Revelli, A. et al. Resonant inelastic x-ray incarnation of Young’s double-slit experiment. Sci. Adv. 5, eaav4020 (2019).Article CAS PubMed PubMed Central Google Scholar Magnaterra, M. et al. Quasimolecular Jtet = 3/2 moments in the cluster Mott insulator GaTa4Se8. Phys. Rev. Lett. 133, 046501 (2024).Article CAS PubMed Google Scholar Blumberg, G. et al. Two-magnon Raman scattering in cuprate superconductors: evolution of magnetic fluctuations with doping. Phys. Rev. B 49, 13295 (1994).Article CAS Google Scholar Lou, X., Li, J. & Wu, N. Evolution of two-magnon bound states in a higher-spin ferromagnetic chain with single-ion anisotropy: a complete solution. Phys. Rev. B 110, L100404 (2024).Article CAS Google Scholar Fogh, E. et al. Field-induced bound-state condensation and spin-nematic phase in SrCu2(BO3)2 revealed by neutron scattering up to 25.9 T. Nat. Commun. 15, 442 (2024).Article CAS PubMed PubMed Central Google Scholar Fradkin, E., Kivelson, S. A. & Tranquada, J. M. Colloquium: theory of intertwined orders in high temperature superconductors. Rev. Mod. Phys. 87, 457–482 (2015).Article CAS Google Scholar Fernandes, R. M., Orth, P. P. & Schmalian, J. Intertwinned vestigial order in quantum materials: nematicity and beyond. Annu. Rev. Condens. Matter Phys. 10, 133–154 (2019).Article Google Scholar Kim, J.-K. et al. Resonant inelastic X-ray scattering endstation at the 1C beamline of Pohang Light Source II. J. Synchrotron Radiat. 30, 643–649 (2023).Article CAS PubMed PubMed Central Google Scholar Download referencesWe thank K. Hwang, E. G. Moon, N. Perkins, Y. Li and I. Herbut for insightful discussions. This work was supported by a National Research Foundation (NRF) of Korea grant funded by the Korean government (RS-2024-00360303), the Basic Science Research Program through the NRF of Korea funded by the Ministry of Education (2022R1I1A1A01056493) and the Samsung Science and Technology Foundation under project no. SSTF-BA2201-04. The use of the APS at Argonne National Laboratory was supported by the US Department of Energy under contract no. DE-AC02-06CH11357. We acknowledge the ESRF for providing synchrotron radiation facilities under proposal no. HC-4054, and we thank F. Gerbon for assistance and support in using beamline ID20. S.J. and G.Y.C. are supported by the Samsung Science and Technology Foundation under project no. SSTF-BA2401-03; the NRF of Korea (grant nos RS-2023-00208291, RS-2024-00410027, 2023M3K5A1094810, RS-2023-NR119931, RS-2024-00444725, RS-2023-00256050, RS-2025-08542968 and IRS-2025-25453111) funded by the Korean government (the Ministry of Science and ICT, MSIT); the Air Force Office of Scientific Research under award no. FA23862514026; and the Institute of Basic Science under project code IBS-R014-D1. B.H.K. was supported by the Institute for Basic Science in the Republic of Korea under project no. IBS-R024-D1. The works at Seoul National University were supported by the Leading Researcher Program of the NRF of Korea (grant no. RS-2020-NR049405).These authors contributed equally: Junyoung Kwon, Jaehwon Kim, Gwansuk Oh, Seyoung Jin, Kwangrae Kim, Hoon Kim.Department of Physics, Pohang University of Science and Technology, Pohang, KoreaJunyoung Kwon, Jaehwon Kim, Gwansuk Oh, Seyoung Jin, Kwangrae Kim, Hoon Kim, Seunghyeok Ha, Hyun-Woo J. Kim & B. J. KimCenter for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang, KoreaSeyoung Jin & Gil Young ChoDepartment of Physics, Hanyang University, Seoul, KoreaGiBaik SimESRF, The European Synchrotron, Grenoble, FranceBjörn Wehinger, Gaston Garbarino, Christoph J. Sahle & Alessandro LongoInstitute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, Karlsruhe, GermanyNour Maraytta, Michael Merz & Matthieu Le TaconKarlsruhe Nano Micro Facility, Karlsruhe Institute of Technology, Karlsruhe, GermanyMichael MerzIstituto per lo Studio dei Materiali Nanostrutturati, Consiglio Nazionale delle Ricerche, Palermo, ItalyAlessandro LongoAdvanced Photon Source, Argonne National Laboratory, Lemont, IL, USAJungho KimDepartment of Physics, Chonnam National University, Gwangju, KoreaAra GoDepartment of Physics, Korea Advanced Institute of Science and Technology, Daejeon, KoreaGil Young ChoCenter for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, KoreaBeom Hyun KimDepartment of Physics and Astronomy, Seoul National University, Seoul, KoreaBeom Hyun KimSearch 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 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 ScholarB.J.K. conceived and managed the project. B.H.K. and G.Y.C. planned the theoretical project. J. Kwon grew single crystals and performed RIXS experiments with help from C.J.S., A.L. and Jungho Kim; Jaehwon Kim and B.J.K. performed symmetry analysis; G.O., K.K. and H.K. performed Raman experiments; J. Kwon, Jaehwon Kim, S.H. and H.-W.J.K. performed resonant X-ray diffraction experiments; S.J. and G.Y.C. performed mean-field calculations with help from G.B.S. and A.G.; B.H.K. performed exact diagonalization calculations; and B.W., G.G., N.M., M.M. and M.L.T. performed X-ray diffraction experiments. B.J.K. wrote the manuscript with input from all authors.Correspondence to Gil Young Cho, Beom Hyun Kim or B. J. Kim.The authors declare no competing interests.Nature Materials thanks the anonymous reviewers 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.Wavefunction, Schmidt coefficients, Schmidt basis states, and spin multipoles for states with AI+E nematic (a), and AI+T2 nematic (b) orders. c, The von-Neumann entanglement entropy SE calculated from AI, E nematic, T2 nematic, AI+E nematic, and AI+T2 nematic.Wavefunction, Schmidt coefficients, Schmidt basis states, and spin multipoles for states with AI (a), and E nematic (b) orders. Given the large number of contributing states, only the 20 basis states with the largest weights are shown.a, The temperature dependence of (0 0 10) magnetic Bragg peak measured (blue) at an azimuthal angle of 135∘ (defined to be zero when (1 0 0) is in the scattering plane), where anisotropic tensor of susceptibility (ATS) scattering is minimized. Corresponding phase transition observed by four-probe resistance measurements (black) are overlaid for comparison. b, Azimuthal-angle dependence of the (0 0 10) magnetic Bragg peak intensity. The contribution from the AIAO order to the scattering intensity is isolated by taking the difference (green) between the profiles measured above (red) and below (blue) TC. The AIAO order exhibits no azimuthal angle dependence16.a, False color map of RIXS intensity measured at 6 K along high symmetry points. Yellow circles indicate single-magnon energies determined from fitting the data. b, Stack plot of the energy spectra. The spectra are measured around Γ point at (2 -2 12). c, Γ point spectrum is fitted to elastic (Gaussian), magnon (Lorentzian), and higher-energy excitations (Gaussian convoluted with exponential decay).Comparison of the spectra taken from samples grown at the optimal growth condition (Sample 1) and at a suboptimal condition (Sample 2).Raman spectra below 30 meV measured at temperatures above(upper) and below(lower) 205 K. The total intensity peaks at 205 (blue). CEF of Nd at ≈ 25 meV is resolved at low temperatures.Supplementary Sections 1–8, Figs. 1 and 2 and Tables 1–16.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 permissionsKwon, J., Kim, J., Oh, G. et al. Intertwined orders in a quantum-entangled metal. Nat. Mater. (2026). https://doi.org/10.1038/s41563-025-02475-5Download citationReceived: 07 May 2025Accepted: 18 December 2025Published: 27 January 2026Version of record: 27 January 2026DOI: https://doi.org/10.1038/s41563-025-02475-5Anyone 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