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The Heisenberg triangular-lattice quantum spin liquid and its phase transitions to nearby magnetic orders have received much theoretical attention, but clear experimental manifestations of these states are rare. Here we demonstrate that a spin-half delafossite material, namely, KYbSe 2 , shows close proximity to the triangular-lattice Heisenberg quantum spin liquid. Using neutron scattering, we identify a diffuse continuum with a sharp lower bound within the measured spectra. Applying entanglement witnesses to the data indicates multipartite entanglement spread between its neighbours, and an analysis of its magnetic-exchange couplings reveals close proximity to the theoretical quantum spin-liquid phase. The key features of the data are reproduced by Schwinger boson theory and tensor network calculations with a substantial next-nearest-neighbour coupling. The strength of the dynamical structure factor at the Brillouin-zone K point shows a scaling collapse down to 0.3 K, indicating the existence of a second-order quantum phase transition. Comparing this with previous theoretical work suggests that the proximate phase at a larger next-nearest-neighbour coupling is a gapped Z 2 spin liquid, resolving a long-debated issue. A detailed analysis of inelastic neutron scattering data, including the evaluation of entanglement witnesses used in quantum information theory, supports the proposal that the triangular-lattice antiferromagnet KYbSe 2 is close to a spin-liquid phase.

Antiferromagnetically coupled S = 1/2 spins on an isotropic triangular lattice are the paradigm of frustrated quantum magnetism, but structurally ideal realizations are rare. Here, we investigate NaYbO2, which hosts an ideal triangular lattice of effective Jeff = 1/2 moments with no inherent site disorder. No signatures of conventional magnetic order appear down to 50 mK, strongly suggesting a quantum spin liquid ground state. We observe a two-peak specific heat and a nearly quadratic temperature dependence, in agreement with expectations for a two-dimensional Dirac spin liquid. Application of a magnetic field strongly perturbs the quantum disordered ground state and induces a clear transition into a collinear ordered state, consistent with a long-predicted up–up–down structure for a triangular-lattice XXZ Hamiltonian driven by quantum fluctuations. The observation of spin liquid signatures in zero field and quantum-induced ordering in intermediate fields in the same compound demonstrates an intrinsically quantum disordered ground state. We conclude that NaYbO2 is a model, versatile platform for exploring spin liquid physics with full tunability of field and temperature.

The Kitaev model with an applied magnetic field in the H∥[111] direction shows two transitions: from a nonabelian gapped quantum spin liquid (QSL) to a gapless QSL at Hc1 ≃ 0.2K and a second transition at a higher field Hc2 ≃ 0.35K to a gapped partially polarized phase, where K is the strength of the Kitaev exchange interaction. We identify the intermediate phase to be a gapless U(1) QSL and determine the spin structure function S(k) and the Fermi surface εS F(k) of the gapless spinons using the density matrix renormalization group (DMRG) method for large honeycomb clusters. Further calculations of static spin-spin correlations, magnetization, spin susceptibility, and finite temperature-specific heat and entropy corroborate the gapped and gapless nature of the different field-dependent phases. In the intermediate phase, the spin-spin correlations decay as a power law with distance, indicative of a gapless phase

Recently the Rydberg blockade effect has been utilized to realize quantum spin liquid (QSL) on a kagome lattice. Evidence of QSL has been obtained experimentally by directly measuring non-local string order. In this paper, we report a Bardeen–Cooper–Schrieffer (BCS)-type variational wave function study of the spin liquid state in this model. This wave function is motivated by mapping the Rydberg blockade model to a lattice gauge theory, where the local gauge conservations replace the role of constraints from the Rydberg blockade. We determine the variational parameter from the experimental measurement of the Rydberg atom population. Then we compare the predictions of this deterministic wave function with the experimental measurements of non-local string order. Combining the measurements on both open and closed strings, we extract the fluctuations only associated with the closed-loop as an indicator of the topological order. The prediction from our wave function agrees reasonably well with the experimental data, with only one fitting parameter determined by measurement of Rydberg atom population. Our variational wave function provides a simple and intuitive picture of the QSL in this system that can be generalized to similar spin liquid phases in other lattice geometry.

Currently under active study in condensed matter physics, both theoretically and experimentally, are quantum spin liquid (QSL) states, in which no long-range magnetic ordering appears at low temperatures due to strong quantum fluctuations of the magnetic moments. The existing QSL candidates all have their intrinsic disadvantages, however, and solid evidence for quantum fluctuations is scarce. Here, we report a previously unreported compound, Na₂BaCo(PO₄)₂, a geometrically frustrated system with effective spin-1/2 local moments for Co2+ ions on an isotropic 2-dimensional (2D) triangular lattice. Magnetic susceptibility and neutron scattering experiments show no magnetic ordering down to 0.05 K. Thermodynamic measurements show that there is a tremendous amount of magnetic entropy present below 1 K in 0-applied magnetic field. The presence of localized low-energy spin fluctuations is revealed by inelastic neutron measurements. At low applied fields, these spin excitations are confined to low energy and contribute to the anomalously large specific heat. In larger applied fields, the system reverts to normal behavior as evident by both neutron and thermodynamic results. Our experimental characterization thus reveals that this material is an excellent candidate for the experimental realization of a QSL state.

A geometrically frustrated (GF) magnet consists of localised magnetic moments, spins, whose orientation cannot be arranged to simultaneously minimise their interaction energies. Such materials may host novel fascinating phases of matter, such as fluid-like states called quantum spin-liquids. GF magnets have, like all solid-state systems, randomly located impurities whose magnetic moments may “freeze” at low temperatures, making the system enter a spin-glass state. We analyse the available data for spin-glass transitions in GF materials and find a surprising trend: the glass-transition temperature grows with decreasing impurity concentration and reaches a finite value in the impurity-free limit at a previously unidentified, “hidden”, energy scale. We propose a scenario in which the interplay of interactions and entropy leads to a crossover in the permeability of the medium that assists glass freezing at low temperatures. This low-temperature, “eminuscent”, phase may obscure or even destroy the widely-sought spin-liquid states in rather clean systems. A spin-glass forms in frustrated magnetic systems when at low temperatures impurity sites “freeze” into a random spin configuration. Here, by looking back at previous experimental results, Syzranov and Ramirez show that the glass-transition temperature grows with decreasing impurity concentration.

We determine conditions on the filling of electrons in a crystalline lattice to obtain the equivalent of a band insulator—a gapped insulator with neither symmetry breaking nor fractionalized excitations. We allow for strong interactions, which precludes a free particle description. Previous approaches that extend the Lieb–Schultz–Mattis argument invoked spin conservation in an essential way and cannot be applied to the physically interesting case of spin-orbit coupled systems. Here we introduce two approaches: The first one is an entanglement-based scheme, and the second one studies the system on an appropriate flat “Bieberbach” manifold to obtain the filling conditions for all 230 space groups. These approaches assume only time reversal rather than spin rotation invariance. The results depend crucially on whether the crystal symmetry is symmorphic. Our results clarify when one may infer the existence of an exotic ground state based on the absence of order, and we point out applications to experimentally realized materials. Extensions to new situations involving purely spin models are also mentioned.

A spin-1/2 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 Q = M 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.

We have successfully synthesized the new S = 1 2 anisotropic kagome antiferromagnet ZnCu3(OH)6SO4 and determined its structure by synchrotron x-ray diffraction. No magnetic ordering is observed down to 50 mK, despite a moderately high Weiss temperature of w ∼ −79 K, indicating that the compound is a new quantum spin liquid (QSL) candidate. A linear temperature dependence of the magnetic heat capacity is found at 6 ∼ 15 K and below 0.6 K. Temperature-independent intrinsic susceptibilities are observed exactly in both temperature ranges. This consistently suggests a gapless QSL below 0.6 K, which may evolve from an unconventional quantum spin state at higher temperatures (6 ∼ 15 K).

We report a comprehensive investigation of the frustrated magnetism on the delafossite oxides, α -CrOOH and α -CrOOD, which experimentally realize the S = 3/2 nearly-Heisenberg antiferromagnetic ( J 1 > 0) model on a triangular lattice with weak single-ion anisotropy ( D ). The electron spin resonance (ESR), neutron scattering, and specific heat ( C m ) measurements on both α -CrOOH and α -CrOOD consistently indicate that the long-range 120° Néel order is significantly suppressed and both systems are in the vicinity of a spin-liquid phase with C m ∼ T 2 at low temperatures. The strength of D is quantitatively determined from fitting the high-temperature ESR linewidth and magnetic susceptibility, and its minus sign ( D < 0, easy-axis type) is suggested by the low-energy ( E ⩽ 2 meV) spin excitations. This easy-axis anisotropy ( D / J 1 ∼ −5%) competes with the 120° Néel order and thus enhances the quantum spin fluctuations at low temperatures.