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Register a new userDynamical Correlations of the Kagome S=1/2 Heisenberg Quantum Antiferromagnet
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We determine dynamical response functions of the S=1/2 Heisenberg quantum antiferromagnet on the kagome lattice based on large-scale exact diagonalizations combined with a continued fraction technique. The dynamical spin structure factor has important spectral weight predominantly along the boundary of the extended Brillouin zone and energy scans reveal broad response extending over a range of 2 sim 3J concomitant with pronounced intensity at lowest available energies. Dispersive features are largely absent. Dynamical singlet correlations -- which are relevant for inelastic light probes -- reveal a similar broad response, with a high intensity at low frequencies omega/J lesssim 0.2J. These low energy singlet excitations do however not seem to favor a specific valence bond crystal, but instead spread over many symmetry allowed eigenstates.
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Spin liquids occuring in 2D frustrated spin systems were initially assumed to appear at strongest frustration, but evidence grows that they more likely intervene at transitions between two different types of order. To identify if this is more general, we here analyze a generalization of the spatially anisotropic triangular lattice (SATL) with antiferromagnetic Heisenberg interactions, the spatially emph{completely} anisotropic triangular lattice (SCATL). Using Takahashis modified spin-wave theory, complemented by exact diagonalizations, we find indications that indeed different kinds of order are always separated by disordered phases. Our results further suggest that two gapped non-magnetic phases, identified as distinct in the SATL, are actually continuously connected via the additional anisotropy of the SCATL. Finally, measurements on several materials found magnetic long-range order where calculations on the SATL predict disordered behavior. Our results suggest a simple explanation through the additional anisotropy of the SCATL, which locates the corresponding parameter values in ordered phases. The studied model might therefore not only yield fundamental insight into quantum disordered phases, but should also be relevant for experiments on the quest for spin liquids.
We believe that a necessary first step in understanding the ground state properties of the spin-${scriptstylefrac{1}{2}}$ kagome Heisenberg antiferromagnet is a better understanding of this models very large number of low energy singlet states. A description of the low energy states that is both accurate and amenable for numerical work may ultimately prove to have greater value than knowing only what these properties are, in particular when these turn on the delicate balance of many small energies. We demonstrate how this program would be implemented using the basis of spin-singlet dimerized states, though other bases that have been proposed may serve the same purpose. The quality of a basis is evaluated by its participation in all the low energy singlets, not just the ground state. From an experimental perspective, and again in light of the small energy scales involved, methods that can deliver all the low energy states promise more robust predictions than methods that only refine a fraction of these states.
The magnetic properties of alkali-metal peroxychromate K$_2$NaCrO$_8$ are governed by the $S = 1/2$ pentavalent chromium cation, Cr$^{5+}$. Specific heat, magnetocalorimetry, ac magnetic susceptibility, torque magnetometry, and inelastic neutron scattering data have been acquired over a wide range of temperature, down to 60 mK, and magnetic field, up to 18 T. The magnetic interactions are quasi-two-dimensional prior to long-range ordering, where $T_N = 1.66$ K in $H = 0$. In the $T to 0$ limit, the magnetic field tuned antiferromagnetic-ferromagnetic phase transition suggests a critical field $H_c = 7.270$ T and a critical exponent $alpha = 0.481 pm 0.004$. The neutron data indicate the magnetic interactions may extend over intra-planar nearest-neighbors and inter-planar next-nearest-neighbor spins.
Temperature-dependent dynamical spin correlations, which can be readily accessed via a variety of experimental techniques, hold the potential of offering a unique fingerprint of quantum spin liquids and other intriguing dynamical states. In this work we present an in-depth study of the temperature-dependent dynamical spin structure factor $S({bf q}, omega)$ of the antiferromagnetic (AFM) Heisenberg spin-1/2 model on the kagome lattice with additional Dzyaloshinskii--Moriya (DM) interactions. Using the finite-temperature Lanczos method on lattices with up to $N = 30$ sites we find that even without DM interactions, chiral low-energy spin fluctuations of the $120^circ$ AFM order parameter dominate the dynamical response. This leads to a nontrivial frequency dependence of $S({bf q}, omega)$ and the appearance of a pronounced low-frequency mode at the M point of the extended Brillouin zone. Adding an out-of-plane DM interactions $D^z$ gives rise to an anisotropic dynamical response, a softening of in-plane spin fluctuations, and, ultimately, the onset of a coplanar AFM ground-state order at $D^z > 0.1 J$. Our results are in very good agreement with existing inelastic neutron scattering and temperature-dependent NMR spin-lattice relaxation rate ($1/T_1$) data on the paradigmatic kagome AFM herbertsmithite, where the effect of its small $D^z$ on the dynamical spin correlations is shown to be rather small, as well as with $1/T_1$ data on the novel kagome AFM YCu$_3$(OH)$_6$Cl$_3$, where its substantial $D^z approx 0.25 J$ interaction is found to strongly affect the spin dynamics.
We investigate the spin-1/2 Heisenberg model on a rectangular lattice, using the Gutzwiller projected variational wave function known as the staggered flux state. Using Monte Carlo techniques, the variational parameters and static spin-structure factor for different coupling anisotropies $gamma=J_y/J_x$ are calculated. We observe a gradual evolution of the ground state energy towards a value which is very close to the 1D estimate provided by the Bethe ansatz and a good agreement between the finite size scaling of the energies. The spin-spin correlation functions exhibit a power-law decay with varying exponents for different anisotropies. Though the lack of Neel order makes the staggered flux state energetically unfavorable in the symmetric case $gamma=1$, it appears to capture the essence of the system close to 1D. Hence we believe that the staggered flux state provides an interesting starting point to explore the crossover from quantum disordered chains to the Neel ordered 2D square lattices.
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