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arXiv:2507.04375

Intertwined Orders in a Quantum-Entangled Metal

Kwon, Junyoung, Jaehwon Kim, Oh, Gwansuk, Jin, Seyoung, Kwangrae Kim, Kim, Hoon, Seunghyeok Ha, Hyun-Woo J. Kim, GiBaik Sim, Björn Wehinger, GARBARINO Gaston Leonel, Nour Maraytta, Michael Merz, M. Le Tacon, Christoph J. Sahle, Alessandro Longo, Jungho Kim, Ara Go, Gil Young Cho, Beom Hyun Kim, Jin-Kwang Kim

Published Jul 6, 2025• 0 citations

Abstract

Entanglement underpins quantum information processing and computing, yet its experimental quantification in complex, many-body condensed matter systems remains a considerable challenge. Here, we reveal a highly entangled electronic phase proximate to a quantum metal-insulator transition, identified by resonant inelastic x-ray scattering interferometry. This approach reveals that entanglement across atomic sites generates characteristic interference patterns, which our model accurately reproduces, enabling extraction of a full entanglement spectrum and resolution of the underlying quantum states. Our analysis of the pyrochlore iridate Nd2Ir2O7 demonstrates that the system undergoes pronounced quantum fluctuations in its spin, orbital and charge degrees of freedom, even in the presence of a long-range 'all-in-all-out' antiferromagnetic order. Importantly, the observed entanglement signatures facilitate the coexistence of multiple exotic symmetry-breaking orders. Complementary investigations using Raman spectroscopy corroborate the presence of these hidden orders and their emergent excitations. In particular, we observe a two-magnon-bound state below the lowest single-magnon excitation energy, which, together with split phonon modes, provides strong evidence for cubic symmetry-breaking orders of magnetic origin juxtaposed with the all-in-all-out order. Our work thus establishes a direct link between quantum entanglement and emergent unconventional orders, opening new avenues for investigating quantum materials.

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Entanglement underpins quantum information processing and computing, yet its experimental quantification in complex, many-body condensed matter systems remains a considerable challenge. Here, we reveal a highly entangled electronic phase proximate to a quantum metal-insulator transition, identified by resonant inelastic x-ray scattering interferometry. This approach reveals that entanglement across atomic sites generates characteristic interference patterns, which our model accurately reproduces, enabling extraction of a full entanglement spectrum and resolution of the underlying quantum states. Our analysis of the pyrochlore iridate Nd2Ir2O7 demonstrates that the system undergoes pronounced quantum fluctuations in its spin, orbital and charge degrees of freedom, even in the presence of a long-range 'all-in-all-out' antiferromagnetic order. Importantly, the observed entanglement signatures facilitate the coexistence of multiple exotic symmetry-breaking orders. Complementary investigations using Raman spectroscopy corroborate the presence of these hidden orders and their emergent excitations. In particular, we observe a two-magnon-bound state below the lowest single-magnon excitation energy, which, together with split phonon modes, provides strong evidence for cubic symmetry-breaking orders of magnetic origin juxtaposed with the all-in-all-out order. Our work thus establishes a direct link between quantum entanglement and emergent unconventional orders, opening new avenues for investigating quantum materials.

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Low-dimensional copper oxide lattices naturally manifest electronic states with strong short range quantum entanglement, which are known to lead to remarkable emergent material properties. However the nanometer scale many-body wavefunction is challenging to measure or manipulate in a simple way. In this study, X-ray induced

dd

electronic transitions are used to suppress spin entanglement across a single lattice site in the spin-1/2 antiferromagnetic chain compound SrCuO

_2

, revealing a class of cuprate magnetic excitations that result from breaking the spin chain. These measurements are the first to employ two closely spaced X-ray resonances of copper (M

_2

and M

_3

) as a form of natural 2-slit interferometer to distinguish between different types of electronic transition and resolve how they influence the dynamics of nearby spin-entangled electrons.

Quantum materials are believed to host highly entangled states of matter, but probing and quantifying such entanglement has long remained experimentally elusive. Here, we use resonant inelastic X-ray scattering (RIXS) as a probe of multipartite spin entanglement. By projecting the RIXS cross section onto the appropriate spin excitation channel, we show that the Quantum Fisher Information can be extracted directly from the measured spin fluctuation spectrum. We detect at least 7-partite spin entanglement in the model one-dimensional cuprate Sr

_2

CuO

_3

, revealing one of the largest entanglement depths yet reported in a solid. The observed entanglement depth agrees with Hubbard-model expectations and persists to elevated temperatures. Our results establish RIXS as an experimental probe of many-body spin entanglement and provide a platform for extensions to charge and orbital sectors and nonequilibrium settings.

In this doctoral dissertation, we consider the significance of spin-orbit coupling for the phases of matter which arise for strongly correlated electrons. We explore emergent behavior in quantum many-body systems, including symmetry-breaking orders, quantum spin liquids, and unconventional superconductivity. Our study is cemented by a particular class of Mott-insulating materials, centered around a family of two- and three-dimensional iridium oxides, whose honeycomb-like lattice structure admits peculiar magnetic interactions, the so-called Kitaev exchange. By analyzing recent experiments on these compounds, we show that this unconventional exchange is the key ingredient in describing their magnetism, and then use a combination of numerical and analytical techniques to investigate the implications for the phase diagram as well as the physics of the proximate three-dimensional quantum spin liquid phases. These long-ranged-entangled fractionalized phases should exhibit special features, including finite-temperature stability as well as unconventional high-Tc superconductivity upon charge-doping, which should aid future experimental searches for spin liquid physics. Our study explores the nature of frustration and fractionalization which can arise in quantum systems in the presence of strong spin-orbit coupling.

The spin nematic phase, characterized by long-range order of spin quadrupole moments in the absence of dipolar magnetism, presents a significant challenge for conventional experimental detection. We propose a novel method to detect this elusive order in quantum magnets with an illustration in the spin-1 triangular lattice Mott insulator. By integrating out the phonon degrees of freedom, we obtain a phase diagram with substantially enlarged regions for the spin-nematic and spin-nematic-supersolid phases. We then demonstrate that through the spin-lattice coupling, the emergence of spin nematic order imprints a distinctive signature onto the phonon spectra, providing a clear spectroscopic signature for the quadrupolar order accessible via Raman or inelastic X-ray scattering. Our formalism offers a direct and powerful method to uncover the hidden spin nematicity, opening a new pathway for diagnosing multipolar orders in quantum magnets.