Nature of the Spin Liquid Ground State in a Breathing Kagome Compound Studied by NMR and Series Expansion.

In the vanadium oxyfluoride compound (NH_{4})_{2}[C_{7}H_{14}N][V_{7}O_{6}F_{18}] (DQVOF), the V^{4+} (3d^{1}, S=1/2) ions realize a unique, highly frustrated breathing kagome lattice composed of alternately sized, corner-sharing equilateral triangles. Here we present an ^{17}O NMR study of DQVOF, which isolates the local susceptibility of the breathing kagome network. By a fit to series expansion, we extract the ratio of the interactions within the breathing kagome plane, J_{∇}/J_{Δ}=0.55(4), and the mean antiferromagnetic interaction J[over ¯]=60(7) K. Spin lattice (T_{1}) measurements reveal an essentially gapless excitation spectrum with a maximum gap Δ/J[over ¯]=0.007(7). Our study provides new impetus for further theoretical investigations in order to establish whether the gapless spin liquid behavior displayed by DQVOF is intrinsic to its breathing kagome lattice or whether it is due to perturbations to this model, such as a residual coupling of the V^{4+} ions in the breathing kagome planes to the interlayer V^{3+} (S=1) spins.

Confidence and efficiency scaling in variational quantum Monte Carlo calculations.

Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time-discretized diffusion process. We present a robust and practical method to determine the effective variance of general observables and show how to verify the equilibrium hypothesis by the Kolmogorov-Smirnov test. We then derive scaling laws of the efficiency illustrated by variational Monte Carlo calculations on the two-dimensional electron gas.

Spin susceptibility of quantum magnets from high to low temperatures.

We explain how and why all thermodynamic properties of spin systems can be computed in one and two dimensions in the whole range of temperatures overcoming the divergence towards zero temperature of the standard high-temperature series expansions (HTEs). The method relies on an approximation of the entropy versus energy (microcanonical potential function) on the whole range of energies. The success is related to the intrinsic physical constraints on the entropy function and a careful treatment of the boundary behaviors. This method is benchmarked against two one-dimensional solvable models: the Ising model in longitudinal field and the XY model in a transverse field. With ten terms in the HTE, we find a spin susceptibility within a few percent of the exact results over the entire range of temperatures. The method is then applied to two two-dimensional models: the supposedly gapped Heisenberg model and the J(1)-J(2)-J(d) model on the kagome lattice.

Hartree-Fock ground state phase diagram of jellium.

We calculate the ground state phase diagram of the homogeneous electron gas in three dimensions within the Hartree-Fock approximation and show that broken symmetry states are energetically favored at any density against the homogeneous Fermi gas state with isotropic Fermi surface. At high density, we find metallic spin-unpolarized solutions where electronic charge and spin density form an incommensurate crystal having more crystal sites than electrons. For r(s)→0, our solutions approach pure spin-density waves, whereas the commensurate Wigner crystal is favored at lower densities, r(s)≳3.4. Decreasing the density, the system undergoes several structural phase transitions with different lattice symmetries. The polarization transition occurs around r(s)≈8.5.

Kapellasite: a kagome quantum spin liquid with competing interactions.

Magnetic susceptibility, NMR, muon spin relaxation, and inelastic neutron scattering measurements show that kapellasite, Cu3Zn(OH)6Cl2, a geometrically frustrated spin-1/2 kagome antiferromagnet polymorphic with herbertsmithite, is a gapless spin liquid showing unusual dynamic short-range correlations of noncoplanar cuboc2 type which persist down to 20 mK. The Hamiltonian is determined from a fit of a high-temperature series expansion to bulk susceptibility data and possesses competing exchange interactions. The magnetic specific heat calculated from these exchange couplings is in good agreement with experiment. The temperature dependence of the magnetic structure factor and the muon relaxation rate are calculated in a Schwinger-boson approach and compared to experimental results.

Ring exchanges and the supersolid phase of 4He.

Using path integral Monte Carlo simulations we calculate exchange frequencies in bulk hcp 4He as atoms undergo ring exchange. We fit the frequencies to a lattice model and examine whether such atoms could become a supersolid, that is, have a nonclassical rotational inertia. We find that the scaling with respect to the number of exchanging atoms is such that superfluid behavior will not be observed in a perfect 4He crystal.

Exchange frequencies in the 2D Wigner crystal.

Using path integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a "clean" 2D Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2D (3)He. Using the resulting multispin exchange model we find the spin Hamiltonian for r(s) < or = 175 +/- 10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic.

Magnetothermodynamics of the spin- 1 / 2 Kagome antiferromagnet

In this paper, we use a new hybrid method to compute the thermodynamic behavior of the spin- 1 / 2 Kagome antiferromagnet under the influence of a large external magnetic field. We find a T2 low-temperature behavior and a very low sensitivity of the specific heat to a strong external magnetic field. We display clear evidence that this low-temperature magnetothermal effect is associated with the existence of low-lying fluctuating singlets, but also that the whole picture ( T2 behavior of C(v) and the thermally activated spin susceptibility) implies contribution of both nonmagnetic and magnetic excitations. Comparison with experiments is made.