The discovery of massless Dirac electrons in graphene and topological Dirac-Weyl materials has prompted a broad search for bosonic analogues of such Dirac particles. Recent experiments have found evidence for Dirac magnons above an Ising-like ferromagnetic ground state in a twodimensional (2D) kagome lattice magnet and in the van der Waals layered honeycomb crystal CrI3, and in a 3D Heisenberg magnet Cu3TeO6. Here we report on our inelastic neutron scattering investigation on large single crystals of a stacked honeycomb lattice magnet CoTiO3, which is part of a broad family of ilmenite materials. The magnetically ordered ground state of CoTiO3 features ferromagnetic layers of Co 2+ , stacked antiferromagnetically along the c-axis. We discover that the magnon dispersion relation exhibits strong easy-plane exchange anisotropy and hosts a clear gapless Dirac cone along the edge of the 3D Brillouin zone. Our results establish CoTiO3 as a model pseudospin-1/2 material to study interacting Dirac bosons in a 3D quantum XY magnet.The discoveries of graphene and topological insulators have led to significant advances in our understanding of the properties of electron in solids described by a Dirac equation. In particular, the fruitful analogy between fundamental massless Weyl-Dirac fermions in Nature and electrons in graphene or topological semimetals has allowed physicists to simulate theories of particle physics using tabletop experiments [1][2][3][4][5][6]. Remarkably, the concept of Dirac particles is not limited to electrons or other fermionic quasiparticles, prompting a search for analogues in photonic crystals [7,8], acoustic metamaterials [9], and quantum magnets [10][11][12][13]. In particular, Dirac magnons, or more broadly defined topological magnons [14][15][16][17][18][19], have attracted much attention as platforms to investigate the effect of inter-particle interaction or external perturbations on Dirac bosons, and are proposed to be of potential interest in spintronic applications.In contrast to light and sound, the symmetry broken states and emergent bosonic excitations of quantum magnets depend crucially on dimensionality and spin symmetry, which provides a fertile playground for examining the physics of topological bosons. To date, gapped topological magnons in Ising-like ferromagnets have been reported in a kagome lattice material Cu(1,3bdc) [16] and in a layered honeycomb magnet CrI 3 [17]. On the other hand, magnons exhibiting symmetry protected band crossings have been found only in a single material, a three-dimensional (3D) Heisenberg antiferromagnet Cu 3 TeO 6 [18,20]. It is thus desirable to explore new test-beds with distinct spin symmetries to expand our understanding of the physics of Dirac magnons.In this paper, we present a new model 3D quantum XY magnet realizing gapless Dirac magnons, CoTiO 3 , which has a simple ilmenite crystal structure. The magnetic lattice of Co 2+ ions in CoTiO 3 is a stacked honeycomb lattice, exactly the same as in ABC stacked graphene. Below T N ≈ 38 K, this mate...

We study the disordered Heisenberg spin chain, which exhibits many body localization at strong disorder, in the weak to moderate disorder regime. A continued fraction calculation of dynamical correlations is devised, using a variational extrapolation of recurrents. Good convergence for the infinite chain limit is shown. We find that the local spin correlations decay at long times as C ∼ t −β , while the conductivity exhibits a low frequency power law σ ∼ ω α . The exponents depict subdiffusive behavior β < 1/2, α > 0 at all finite disorders, and convergence to the scaling result, α + 2β = 1, at large disorders.

We study bounds on ratios of fluctuations in steady-state time-reversal heat engines controlled by multi affinities. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always lower-bounded by the relative fluctuations of the input current (heat current absorbed from the hot bath). As a consequence, the ratio between the fluctuations of the output and input currents are bounded both from above and below, where the lower (upper) bound is determined by the square of the averaged efficiency (square of the Carnot efficiency) of the engine. The saturation of the lower bound is achieved in the tight-coupling limit when the determinant of the Onsager response matrix vanishes. Our analysis can be applied to different operational regimes, including engines, refrigerators, and heat pumps. We illustrate our findings in two types of continuous engines: two-terminal coherent thermoelectric junctions and three-terminal quantum absorption refrigerators. Numerical simulations in the far-from-equilibrium regime suggest that these bounds apply more broadly, beyond linear response.

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The doped 1D Kondo Lattice describes complex competition between itinerant and magnetic ordering. The numerically computed wave vector-dependent charge and spin susceptibilities give insights into its low-energy properties. Similar to the prediction of the large N approximation, gapless spin and charge modes appear at the large Fermi wave vector. The highly suppressed spin velocity is a manifestation of "heavy" Luttinger liquid quasiparticles. A low-energy hybridization gap is detected at the small (conduction band) Fermi wave vector. In contrast to the exponential suppression of the Fermi velocity in the large- approximation, we fit the spin velocity by a density-dependent power law of the Kondo coupling. The differences between the large- theory and our numerical results are associated with the emergent magnetic Ruderman-Kittel-Kasuya-Yosida interactions.