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arXiv:2512.18831 · Physical Review Letters

Dynamical Spectral Function of the Kagome Quantum Spin Liquid

Jiahang Hu, Runze Chi, Yibin Guo, B. Normand, Hai-Jun Liao, T. Xiang

cond-mat.str-elquant-phSubmitted Dec 21, 2025• Announced Dec 23, 2025• 0 citations• Revised Aug 17, 2026 (v3)
v1 · Dec 21, 2025v2 · Mar 28, 2026v3 · Aug 17, 2026
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Abstract

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 $J_1$-$J_2$ kagome Heisenberg model and benchmark our results by tracking their evolution across the magnetically ordered and QSL phases. Reducing $|J_2|/J_1$ 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.

Journal reference
Phys. Rev. Lett. 137, 076504 (2026)
DOI
10.1103/fjjf-xspp
Comments
17 pages, 14 figures

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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.
Dynamics and stability of U(1) spin liquids beyond mean-field theory: Triangular-lattice J1J_1J1​-J2J_2J2​ Heisenberg model
Quantum spin liquids (QSLs) are long-range entangled phases of frustrated magnets exhibiting fractionalised spin excitations. In two dimensions, there is limited analytical understanding of their excitation spectra beyond parton mean-field theories, which fail to capture many features of the finite frequency dynamical response. We use a self-consistent mean-field theory combined with the random phase approximation (RPA) for the J1J_1J1​-J2J_2J2​ Heisenberg model on the triangular lattice to describe the strong spinon-spinon interactions of the U(1) Dirac QSL. We obtain quantitative results for the dynamical spin structure factor and phase diagram compatible with comprehensive numerical efforts. We show the continuum response at the Brillouin zone corners is described by a spinon-exciton hybridised with monopole gauge excitations. We further show that the transition from the QSL to 120-degree coplanar order is in the QED3_33​ O(3)-GN universality class. We extend the method to chiral QSLs and XXZ anisotropy, and discuss its broad range of applicability to other models and for describing inelastic neutron scattering experiments in KYbSe2_22​.
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.
A quantum spin liquid (QSL) is an exotic quantum state of matter characterized by fluctuating spins which may exhibit long-range entanglement. Among the possible host candidates for a QSL ground state, the SSS=1/2 kagome lattice antiferromagnet is particularly promising. Using high resolution inelastic neutron scattering measurements on Zn-barlowite (Znx_\mathrm{x}x​Cu4−x_\mathrm{4-x}4−x​(OD)6_\mathrm{6}6​FBr, x≃0.80x\simeq 0.80x≃0.80), we measure a spin excitation spectrum consistent with a QSL ground state. Continuum scattering above $\sim1meVmatchesthatofherbertsmithite(Zn1 meV matches that of herbertsmithite (Zn1meVmatchesthatofherbertsmithite(Zn_\mathrm{x}CuCuCu_\mathrm{4-x}(OD)(OD)(OD)_6ClClCl_2$, x≃0.85x\simeq 0.85x≃0.85), another prominent kagome QSL material, indicating universal spinon excitations. A detailed analysis of the spin-spin correlations, compared with density matrix renormalization group calculations, further indicate a QSL ground state for the physically relevant Hamiltonian parameters. The measured spectra in Zn-barlowite are consistent with gapped behavior with a gap size Δ=1.1(2)Δ= 1.1(2)Δ=1.1(2) meV. Comparison with a simple pair correlation model allows us to clearly distinguish intrinsic kagome correlations from impurity-induced correlations. Our results clarify the behavior that is universal within this important family of QSL candidate materials.
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.
Unraveling the Kagome Antiferromagnetic 3J3J3J Model and Its Materials: An Integrated Approach
We investigate the ground-state and finite-temperature properties of the kagome antiferromagnetic Heisenberg model with three inequivalent couplings, dubbed the 3J3J3J model, which is designed for the candidate Dirac quantum spin liquid (QSL) material YCu3_33​(OH)6_66​Br2_22​[Br1−x_{1-x}1−x​(OH)x_xx​] (see, e.g., Zeng et al., 2024). Employing large-scale density-matrix renormalization group (DMRG) supplemented by neural quantum states (NQS) simulations, we identify an intermediate QSL phase between two magnetically ordered phases. We also find that this QSL is separated from the kagome spin liquid ground state at the isotropic limit. To establish a direct comparison with experiments, we compute the specific heat of the model by means of advanced exponential (XTRG) and tangent-space (tanTRG) thermal tensor-network methods. In the magnetically ordered phase, the specific heat over temperature exhibits a shoulder at a temperature that is a fraction of the coupling strength JhJ_{h}Jh​, which disappears in the QSL phase. These universal behaviors are consistent with the experimentally observed specific heat in 3J3J3J materials for both ordered and QSL candidate samples. Our work thus connects microscopic models with experimentally measurable signatures, exemplifying an integrated approach to understanding QSL phenomena in frustrated quantum magnets~ (see Meng et al., 2026), with 3J3J3J materials serving as a representative case and providing a foundation for future studies.
We combine the pseudofermion functional renormalization group (PFFRG) method with a self-consistent Fock-like mean-field scheme to calculate low-energy effective theories for emergent spinon excitations in spin-1/2 quantum spin liquids. Using effective spin interactions from PFFRG as an input for the Fock equation and allowing for the most general types of free spinon Ans\"atze as classified by the projective symmetry group (PSG) method, we are able to systematically determine spinon band structures for spin-liquid candidate systems beyond mean-field theory. We apply this approach to the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the square lattice and to the antiferromagnetic nearest-neighbor Heisenberg model on the kagome lattice. For the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model, we find that in the regime of maximal frustration a SU(2) $\ensuremath{\pi}$-flux state with Dirac spinons yields the largest mean-field amplitudes. For the kagome model, we identify a gapless Z2{\mathbb{Z}}_{2}Z2​ spin liquid with a small circular spinon Fermi surface and approximate Dirac cones at low but finite energies.