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arXiv:2603.19951

Quantum Fisher Information as a Probe of Critical Scaling in Frustrated Magnets: Signatures from Kagome Quantum Spin Liquid

Zhengbang Zhou, Chengkang Zhou, Menghan Song, Yong Baek Kim, Zi Yang Meng

cond-mat.str-elquant-phSubmitted Mar 20, 2026• Announced Mar 23, 2026• 0 citations
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Abstract

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 $\mathbb{Z}_2$ 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.

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8+6 pages, 4+10 figures

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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.
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.
A spin-[Formula: see text] lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around the [Formula: see text] point in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.
Quantum spin liquids (QSLs) are exotic phases of matter that host fractionalized excitations. It is difficult for local probes to characterize QSL, whereas quantum entanglement can serve as a powerful diagnostic tool due to its nonlocality. The kagome antiferromagnetic Heisenberg model is one of the most studied and experimentally relevant models for QSL, but its solution remains under debate. Here, we perform a numerical Aharonov-Bohm experiment on this model and uncover universal features of the entanglement entropy. By means of the density matrix renormalization group, we reveal the entanglement signatures of emergent Dirac spinons, which are the fractionalized excitations of the QSL. This scheme provides qualitative insights into the nature of kagome QSL and can be used to study other quantum states of matter. As a concrete example, we also benchmark our methods on an interacting quantum critical point between a Dirac semimetal and a charge-ordered phase.
Quantum spin liquids (QSLs) host exotic fractionalized magnetic and gauge-field excitations whose microscopic origins and experimental verification remain frustratingly elusive. In the absence of static magnetic order, the spin excitation spectrum constitutes the crucial probe of QSL behavior, but its theoretical computation is a serious challenge. Here we employ state-of-the-art tensor-network methods to obtain the full dynamical spectral function of the J1J_1J1​-J2J_2J2​ kagome Heisenberg model and benchmark our results by tracking their evolution across the magnetically ordered and QSL phases. Reducing ∣J2∣/J1|J_2|/J_1∣J2​∣/J1​ causes increasingly strong spin-wave renormalization, flattening these modes then merging them into a continuum characteristic of deconfined spinons at all finite energies in the QSL. The low-energy continuum and the occurrence of gap closure at multiple high-symmetry points identify this gapless QSL as the U(1) Dirac spin liquid. These results establish a unified understanding of spin excitations in highly frustrated quantum magnets and provide clear spectral fingerprints for experimental detection in candidate kagome QSL materials.
The nontriviality of quantum spin liquids (QSLs) typically manifests in the nonlocal observables that signify their existence; however, this fact actually casts a shadow on detecting QSLs with experimentally accessible probes. Here, we provide a solution by unbiasedly demonstrating a dynamical signature of anyonic excitations and symmetry fractionalization in QSLs. Employing large-scale quantum Monte Carlo simulation and stochastic analytic continuation, we investigate the extended XXZ model on the kagome lattice, and find out that, across the phase transitions from Z_{2} QSLs to different symmetry breaking phases, spin spectral functions can reveal the presence and condensation of emergent anyonic spinon and vison excitations, in particular, the translational symmetry fractionalization of the latter, which can be served as the dynamical signature of the seemingly ephemeral QSLs in spectroscopic techniques such as inelastic neutron or resonance (inelastic) x-ray scatterings.
The quantum spin liquid (QSL) state, proposed more than three decades ago by Fazekas and Anderson remains surprisingly elusive. Although recent experiments provide a strong evidence of their existence in the frustrated spin systems, the microscopic model for this state is still rare. The extensive theoretical framework, developed over decades, continues to extend further motivated by these and other discoveries from large-scale computer simulations of a relatively small number of models. In this work, we discuss the physics of the ground-state phase diagram of a two-dimensional Kagome lattice spin-1/2 XY model with a four-site ring-exchange interaction using quantum Monte Carlo simulation. We found the second order phase transition from superfluid state to a Z2 quantum spin liquid phase driven by the four-site ring exchange interaction. We have characterized the QSL by its vanishing order parameters such as the spin-spin structure factor, the plaquette-plaquette structure factor. Moreover, we have found the large anomalous exponent ηXY* ≈ 1.325 which belongs to a different universality class other than 3D XY universality class. There is no signal of supersolid phase intervening between the superfluid state and QSL state.