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arXiv:2510.14813 · Nature Communications

Quantum Fisher information as a thermal probe in frustrated magnets through insights from quantum spin ice

Chengkang Zhou, Zhengbang Zhou, Félix Desrochers, Yong Baek Kim, Zi Yang Meng

Published Jun 25, 2026• 0 citations
arXivHTMLPDF

Abstract

Quantum Fisher information (QFI) is a measure of multipartite entanglement accessible via inelastic neutron scattering. Here we demonstrate that QFI reveals thermal and dynamical properties of quantum spin ice (QSI), a three-dimensional quantum spin liquid with fractionalized excitations. By developing a multi-directed loop update quantum Monte Carlo algorithm, along with exact diagonalization and gauge mean-field theory, we compute the QFI for the pyrochlore lattice. The temperature and momentum dependence of QFI maps the phase diagram, distinguishing the ferromagnetic ordered phase, its critical region, the zero-flux QSI, and the π-flux QSI. QFI also captures two crossover scales: from trivial paramagnet to classical spin ice, then to QSI. We discuss the π-flux QSI in light of experiments on cerium-based pyrochlores. Our results suggest that QFI not only detects entanglement but also serves as a sensitive thermal and dynamical probe for frustrated quantum magnets. Quantum Fisher information is a rapidly developing tool for measuring entanglement accessible in inelastic neutron scattering experiments, but its broader utility for characterizing quantum phases remains unclear. Here, the authors propose that temperature and momentum resolved quantum Fisher information can quantitatively map phase boundaries and crossovers in quantum spin ice.

DOI
10.1038/s41467-026-74589-6

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Quantum Fisher information (QFI) is a measure of multipartite entanglement accessible via inelastic neutron scattering. Here we demonstrate that QFI reveals thermal and dynamical properties of quantum spin ice (QSI), a three-dimensional quantum spin liquid with fractionalized excitations. By developing a multi-directed loop update quantum Monte Carlo algorithm, along with exact diagonalization and gauge mean-field theory, we compute the QFI for the pyrochlore lattice. The temperature and momentum dependence of QFI maps the phase diagram, distinguishing the ferromagnetic ordered phase, its critical region, the zero-flux QSI, and the π-flux QSI. QFI also captures two crossover scales: from trivial paramagnet to classical spin ice, then to QSI. We discuss the π-flux QSI in light of experiments on cerium-based pyrochlores. Our results suggest that QFI not only detects entanglement but also serves as a sensitive thermal and dynamical probe for frustrated quantum magnets. Quantum Fisher information is a rapidly developing tool for measuring entanglement accessible in inelastic neutron scattering experiments, but its broader utility for characterizing quantum phases remains unclear. Here, the authors propose that temperature and momentum resolved quantum Fisher information can quantitatively map phase boundaries and crossovers in quantum spin ice.
Quantum Fisher information (QFI) is a measure of multipartite quantum entanglement that can be obtained from inelastic neutron scattering data on quantum magnets. In this work, we demonstrate that the QFI can distinguish an unconventional quantum critical point (QCP) with fractionalization and emergent gauge structure from conventional ones within the Landau paradigm. We compute the QFI, via large-scale quantum Monte Carlo (QMC) simulations and exact diagonalization, in a kagome lattice quantum spin liquid (QSL) model with an XY and a cluster-Ising interactions. When the XY interaction is ferromagetic, the QFI obtained by QMC reveals a large anomalous dimension, which is a fingerprint of the (2+1)d XY∗^\ast∗ universality class for the transition from the ferromagnetic phase to the Z2\mathbb{Z}_2Z2​ QSL. The investigation of thermal and dynamical properties of QFI is further extended to the case of antiferromagnetic XY interaction via exact diagonalization. In this regime, a transition to a possibly distinct QSL phase is suggested via both entanglement-based probes, such as QFI and genuine multipartite negativity, and analyses of the energy spectrum and structure factors. These results not only demonstrate the versatility of QFI in identifying QSL states and unconventional QCPs but also provide useful guidance for future theoretical and experimental studies of frustrated magnets.
Strange metals exemplify highly collective quantum many-body systems that call for new means of characterization, and there is considerable potential for quantum information approaches contributing to the cause. We investigate multipartite entanglement across the quantum phase transition of a Kondo lattice model using the quantum Fisher information (QFI). We show that the QFI associated with the spin components transverse to the order parameter characterizes the destruction of heavy quasiparticles in the Kondo-destroyed magnetic-ordered phase. The physical origin of this observation is elucidated through an analysis of the antiferromagnetic Heisenberg model. We propose to test the results in terms of both unpolarized and polarized inelastic neutron scattering measurements in the ordered part of the heavy fermion phase diagram. Our findings illustrate how different operators of a many-body system can be employed to not only witness multipartite entanglement in different sectors and but also elucidate the overall physics across different parts of the phase diagram.
Quantum Fisher Information (QFI) is a powerful spectroscopic tool to witness many-body quantum entanglement in solid state materials, but it is not always obvious how to relate it to other characteristics of condensed matter systems. In this study we elaborate on the meaning and interpretation of QFI in condensed matter by examining simple theoretical spin systems. We use finite sized spin systems to illustrate that QFI quantifies the momentum- dependent degree of quantum entanglement (that is the entanglement depth at a given wave vector) within a wave function. We subsequently use semiclassical frustrated spin models to show that, in the context of linear spin wave theory (LSWT), QFI quantifies the momentum-dependent degree of magnon squeezing in the ground state. In antiferromagnets with a zero-energy Goldstone mode, LSWT breaks down and QFI (and entanglement depth) diverges at the magnetic ordering wave vector. We also show examples of emergent quantum phases in frustrated spin systems that do not appear in classical phase diagrams. When these emergent phases are approached, QFI diverges across multiple wave vectors in momentum space. Taken together, QFI is not only helpful as a lower bound for entanglement depth, but serves as a momentum-resolved probe of entanglement that offers a novel perspective on quantum critical phenomena.
The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.
In 1935, as part of a broader debate about the interpretation of quantum mechanics, Schrödinger introduced the term “verschränkung” (entanglement) to describe the way in which mutually-exclusive experimental outcomes could be woven together in a single quantum mechanical state. Ninety years later, entanglement is no longer a philosophical curiosity but a technological resource, central to the pursuit of quantum advantage sought in the entanglement of a few hundred qubits. In the context of condensed matter physics, the most celebrated example of entanglement arises in quantum spin liquids (QSL), exotic magnetic phases where, at comparable temperatures, billions of spins can be entangled. The sharpest distinctions between conventional magnetic phases, QSL, and states driven by disorder, are expected to be found in their entanglement properties. Yet exactly what these distinctions are, or how they might be used in experiments, remains poorly understood. In this thesis, we explore how material-based imperfections such as bond disorder and finite temperature affect experimentally accessible entanglement-based diagnostics in models of quantum spin liquids (QSLs). We ask: (1) Can spin liquid states be reliably distinguished from disorder-driven phases using such diagnostics? (2) What can these experimentally accessible entanglement witnesses reveal about the microscopic structure of entanglement in QSLs? In particular, we examine the robustness of these quantum correlations under realistic conditions where thermal fluctuations are unavoidable. In addressing (1), we find that measures like concurrence become unreliable in disordered systems. In contrast, the finite temperature scaling of multipartite diagnostics such as the quantum Fisher information (QFI) provides a more effective means of distinguishing QSLs from competing disorder-dominated phases. For (2), we investigate how the finite temperature behavior of multipartite entanglement measures obtained from semidefinite programming (SDP) methods supports a two step picture for how a high temperature paramagnet crosses over into a QSL ground state. In particular, these results provide a conceptual framework that places quantitative bounds on the temperature window over which candidate materials can be expected to exhibit the characteristic physics of the QSL ground state.
Three dimensional frustrated magnets realized in the rare-earth pyrochlores R_2B_2O_7, R=rare-earth ion, B transition metal ion) have attracted much interest since the discovery of spin ice in Ho_2Ti_2O_7 by Harris et al. Since then, a number of interesting phenomena in pyrochlore magnets have been observed and the interest in these systems, from an experimental and theoretical point of view, has nothing but increased. Perhaps the most appealing and unique possibility is that these systems may realize a quantum disordered phase; a so-called quantum spin ice. Theoretically, it has been predicted by Hermele et al. that a U(1) quantum spin liquid is realized in the XXZ quantum spin ice (with global U(1)xZ_2 symmetry) in the perturbative regime and more recently Savary and Balents have introduced a quantum rotor model with bosonic spinons coupled to U(1)U(1)U(1) gauge fields to describe non-peturbatively the deconfined phase predicted. They studied an anisotropic quantum spin ice (QSI) model which corresponds to the XXZ QSI with an additional anisotropic coupling. They solved the quantum rotor model using a mean-field approximation combined with a large-N approximation and predicted the possibility of a U(1) liquid in addition to an exotic ferromagnetic phase. Further work by Lee et al. has addressed the more complicated fully frustrated XXZ quantum spin ice regime, where all components of the model are frustrated, by using some insights provided by the previous perturbative results. \n \nIn this thesis, we will address the non-perturbative regime of the fully frustrated XXZ QSI beyond the simplest perturbative treatment. We will begin by mapping the quantum spin ice model to a compact U(1) gauge theory with deconfined electric and magnetic monopoles. Neglecting the interaction between the gapless photon excitation and the electric charges, we will study the matter sector with only electric charges, the so-called spinons. Building up on insights provided by high order degenerate perturbation theory calculations, we will construct some symmetric spin liquid ansatz for the static part of the gauge fields. The two novel spin liquids that we construct break time reversal symmetry and thus have a non-trivial chirality. In order to solve the matter sector of the theory and determine the stability of the deconfined phases, we will introduce a novel representation of a XY quantum rotor in terms of ``exclusive" bosons, a representation which is dynamically implemented in the dilute limit. We will benchmark this mapping in different ways by comparing our results with Quantum Monte Carlo simulations and exact diagonalization in some limiting cases. Using this mapping we will compute the region of stability of the U(1) liquid phase of XXZ QSI. Within this mapping we will reproduce qualitatively the results of previous work by finding only the so-called zero and \\pi-flux U(1) liquids in the vicinity of the classical spin ice point, while improving greatly on the estimation of the exchange coupling at which the bosonic spinons condense to form a superfluid phase. In the fully frustrated XXZ QSI, we will provide evidence, using exact diagonalization of the quantum rotor model, that one of the chiral spin liquid may be realized in the strongly correlated and frustrated QSI regime, where all previous approximations break down.