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arXiv:2403.12779 · Nature Physics

Quantum Fisher information in a strange metal

Federico Mazza, Sounak Biswas, Xinlin Yan, Andrey Prokofiev, P. Steffens, Qimiao Si A, Fakher F. Assaad, Silke Buehler Paschen

Published Jun 15, 2026• 4 citations
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Abstract

A strange metal is an exotic state of correlated quantum matter, and intensive efforts are ongoing to understand its nature. Here we show that the quantum Fisher information-a concept from quantum metrology-may provide helpful insights. We use inelastic neutron scattering and quantum Monte Carlo simulations to study quantum critical fluctuations of the Kondo destruction type, which are considered to underlie strange metal behaviour in heavy-fermion compounds. We find that the associated quantum Fisher information increases strongly and without a characteristic scale as the strange metal forms with decreasing temperature. This provides evidence for a quantum state with high multipartite entanglement and offers a positive descriptor of strange metallicity that points towards its microscopic basis. Our work opens a direction for future studies across a range of strange metal platforms.

DOI
10.1038/s41567-026-03298-0

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A strange metal is an exotic state of correlated quantum matter, and intensive efforts are ongoing to understand its nature. Here we show that the quantum Fisher information-a concept from quantum metrology-may provide helpful insights. We use inelastic neutron scattering and quantum Monte Carlo simulations to study quantum critical fluctuations of the Kondo destruction type, which are considered to underlie strange metal behaviour in heavy-fermion compounds. We find that the associated quantum Fisher information increases strongly and without a characteristic scale as the strange metal forms with decreasing temperature. This provides evidence for a quantum state with high multipartite entanglement and offers a positive descriptor of strange metallicity that points towards its microscopic basis. Our work opens a direction for future studies across a range of strange metal platforms.
Strong correlations in matter promote a landscape of quantum phases and associated quantum critical points. For metallic systems, there is increasing recognition that the quantum criticality goes beyond the Landau framework and, thus, further means are needed to characterize the quantum critical fluid. Here we do so by studying an entanglement quantity, the quantum Fisher information, in a strange metal system, focusing on the exemplary case of an Anderson/Kondo lattice model near its Kondo destruction quantum critical point. The spin quantum Fisher information peaks at the quantum critical point and indicates a strongly entangled ground state. Our results are supported by the quantum Fisher information extracted from inelastic neutron scattering measurements in heavy fermion metals. Our work elucidates the loss of quasiparticles in strange metals, opens a quantum information avenue to advance the understanding of metallic quantum criticality in a broad range of strongly correlated systems, and points to a regime of quantum matter to realize amplified entanglement. Strange metals exhibit anomalous electronic and thermodynamic properties near a quantum critical point. Here the authors show theoretically that entanglement quantified by quantum Fisher information is amplified in a strange metal at a quantum critical point, which is supported by analysis of experimental data.
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.
Strange metals appear in a wide range of correlated materials. Electronic localization-delocalization and the expected loss of quasiparticles characterize beyond-Landau metallic quantum critical points and the associated strange metals. Typical settings involve local spins. Systems that contain entwined degrees of freedom offer new platforms to realize unusual forms of quantum criticality. Here, we study the fate of an SU(4) spin-orbital Kondo state in a multipolar Bose-Fermi Kondo model, which provides an effective description of a multipolar Kondo lattice, using a renormalization-group method. We show that at zero temperature, a generic trajectory in the model's parameter space contains two quantum critical points, which are associated with the destruction of Kondo entanglement in the orbital and spin channels, respectively. Our asymptotically exact results reveal an overall phase diagram, provide the theoretical basis to understand puzzling recent experiments of a multipolar heavy fermion metal, and point to a means of designing different forms of quantum criticality and strange metallicity in a variety of strongly correlated systems.
A recent inelastic-neutron-scattering experiment on the heavy-fermion strange metal Ce3Pd20Si6\mathrm{Ce}_3\mathrm{Pd}_{20}\mathrm{Si}_6Ce3​Pd20​Si6​ reports a scale-free increase of the quantum Fisher information (QFI) density as the strange-metal state forms, witnessing high multipartite entanglement. We ask whether this signature is reproduced by the non-injective projection framework of Cosmochrony, and we isolate the structural condition under which it is. We first reduce the QFI density to the projective spectral data: using linear response, the QFI density is a weighted integral of the imaginary part of the dynamical susceptibility, whose infrared behaviour is controlled by the projective stability gap ΔΠ{\Delta_\Pi}ΔΠ​ and the edge spectral weight of the projective stability operator LΠ{L_\Pi}LΠ​. This yields a clean dichotomy. A finite gap forces the QFI density to saturate; a gap that closes with an anomalous edge density of states of exponent aaa forces fQ(T)∼T1−a{f_Q}(T)\sim T^{1-a}fQ​(T)∼T1−a, so that scale-free growth requires a>1a>1a>1. We then evaluate the two ingredients by exact diagonalisation. The single winding sector w=2w=2w=2 reduces to the critical almost-Mathieu (Harper) operator at flux 2/q2/q2/q; its gap closes as ΔΠ∼q−1{\Delta_\Pi}\sim q^{-1}ΔΠ​∼q−1 but its edge spectral dimension is ds→2d_s\to 2ds​→2, giving a→1a\to 1a→1, the marginal boundary, hence only logarithmic growth. The full Cayley substrate of Heis3(Z/qZ){\mathrm{Heis}_3(\mathbb{Z}/q\mathbb{Z})}Heis3​(Z/qZ), whose homogeneous growth dimension is D=4D=4D=4, instead has an edge spectral dimension ds≈4d_s\approx 4ds​≈4, giving a≈2a\approx 2a≈2 and fQ(T)∼T−1{f_Q}(T)\sim T^{-1}fQ​(T)∼T−1, a genuine power law. The conclusion is structural: in this framework the scale-free QFI growth is a property of the full nilpotent substrate and not of any isolated composite, consistent with the collective, multipartite character of the measured entanglement. The required thermal closure ΔΠ(T)∼T{\Delta_\Pi}(T)\sim TΔΠ​(T)∼T is obtained at the level of the effective heat-kernel response: the framework identifies the diffusion scale with inverse temperature, and the induced linear-response flow gives ΔΠ(T)=ds2T{\Delta_\Pi}(T)=\tfrac{d_s}{2}TΔΠ​(T)=2ds​​T, so that the chain from the nilpotent substrate to the linear prediction fQ(T)∼T−1{f_Q}(T)\sim T^{-1}fQ​(T)∼T−1 closes within the effective response regime. The predicted exponent is of the right order but steeper than observed. Numerically, the Born–Infeld bounded-response correction can soften the effective exponent from the linear value αth=1\alpha_{\mathrm{th}}=1αth​=1 towards the observed αexp≈0.7\alpha_{\mathrm{exp}}\approx 0.7αexp​≈0.7, with a size-stable crossing at a partial substrate saturation. The asymptotic exponent and the saturation level realised by the material remain open.
Strange metal behavior has been observed in an expanding list of quantum materials, with heavy fermion metals serving as a prototype setting. Among the intriguing questions is the nature of charge carriers; there is an increasing recognition that the quasiparticles are lost, as captured by Kondo destruction quantum criticality. Among the recent experimental advances is the measurement of shot noise in a heavy-fermion strange metal. We are thus motivated to study current fluctuations by advancing a minimal Bose-Fermi Kondo lattice model, which admits a well-defined large-NNN limit. Showing that the model in equilibrium captures the essential physics of Kondo destruction, we proceed to derive quantum kinetic equations and compute shot noise to the leading nontrivial order in 1/N1/N1/N. Our results reveal a strong suppression of the shot noise at the Kondo destruction quantum critical point, thereby providing the understanding of the striking experiment. Broader implications of our results are discussed.
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.