Diamond lattice Heisenberg antiferromagnet.

We investigate ground-state and high-temperature properties of the nearest-neighbour Heisenberg antiferromagnet on the three-dimensional diamond lattice, using series expansion methods. The ground-state energy and magnetization, as well as the magnon spectrum, are calculated and found to be in good agreement with first-order spin-wave theory, with a quantum renormalization factor of about 1.13. High-temperature series are derived for the free energy, and physical and staggered susceptibilities for spin S = 1/2, 1 and 3/2, and analysed to obtain the corresponding Curie and Néel temperatures.

Are Multiphase Competition and Order by Disorder the Keys to Understanding Yb(2)Ti(2)O(7)?

If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is perhaps no less fascinating, providing an avenue for the exploration and discovery of unconventional behaviors. Here, we study a realistic minimal model where a number of such mechanisms converge, which, incidentally, pertain to the perplexing quantum spin ice candidate Yb(2)Ti(2)O(7). Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder selection, conspire to expand the stability region of a degenerate continuous U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb(2)Ti(2)O(7). The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb(2)Ti(2)O(7) [Lhotel et al., Phys. Rev. B 89, 224419 (2014)]. By combining a gamut of numerical techniques, we obtain compelling evidence that such multiphase competition is a natural engine for the substantial sample-to-sample variability observed in Yb(2)Ti(2)O(7) and is the missing key to ultimately understand the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores.

A frustrated three-dimensional antiferromagnet: stacked J1-J2 layers.

We study a frustrated 3D antiferromagnet of stacked J(1)-J(2) layers. The intermediate 'quantum spin liquid' phase, present in the 2D case, narrows with increasing interlayer coupling and vanishes at a triple point. Beyond this, there is a direct first-order transition from Néel to columnar order. Possible applications to real materials are discussed.

Monte Carlo study of mixed-spin S = (1/2, 1) Ising ferrimagnets.

We investigate Ising ferrimagnets on square and simple cubic lattices with exchange couplings between spins of values S = 1/2 and 1 on neighbouring sites and an additional single-site anisotropy term on the S = 1 sites. Mainly on the basis of a careful and comprehensive Monte Carlo study, we conclude that there is no tricritical point in the two-dimensional case, in contradiction to mean-field predictions and recent series results. However, evidence for a tricritical point is found in the three-dimensional case. In addition, a line of compensation points is found for the simple cubic, but not for the square lattice.

Discerning incompressible and compressible phases of cold atoms in optical lattices.

Experiments with cold atoms trapped in optical lattices offer the potential to realize a variety of novel phases but suffer from severe spatial inhomogeneity that can obscure signatures of new phases of matter and phase boundaries. We use a high temperature series expansion to show that compressibility in the core of a trapped Fermi-Hubbard system is related to measurements of changes in double occupancy. This core compressibility filters out edge effects, offering a direct probe of compressibility independent of inhomogeneity. A comparison with experiments is made.

Ferrimagnetism in the rare-earth iron garnets: a Monte Carlo study.

We investigate classical vector spin models of the rare-earth iron garnet ferrimagnets yttrium iron garnet (YIG) and gadolinium iron garnet (GdIG) using Monte Carlo simulations. Critical temperatures agree well with experiment. A compensation point is observed in GdIG, again in good agreement with experiment.

Symmetry breaking in the collinear phase of the J1-J2 Heisenberg model.

The large J2 limit of the square-lattice J1-J2 Heisenberg antiferromagnet is a classic example of order by disorder where quantum fluctuations select a collinear ground state. Here, we use series expansion methods and a mean-field spin-wave theory to study the excitation spectra in this phase and look for a finite-temperature Ising-like transition, corresponding to a broken symmetry of the square lattice, as first proposed by Chandra et al. [Phys. Rev. Lett. 64, 88 (1990)]]. We find that the spectra reveal the symmetries of the ordered phase. However, we do not find evidence for a finite-T transition. We suggest a scenario for a T=0 transition based on quantum fluctuations.

Realization of a large J(2) quasi-2D spin-half Heisenberg system: Li(2)VOSiO(4).

Exchange couplings are calculated for Li(2)VOSiO(4) using the local-density approximation (LDA). While the sum of in-plane couplings J(1)+J(2) = 9.5+/-1.5 K and the interplane coupling J( perpendicular) approximately 0.2- 0.3 K agree with recent experimental data, the ratio J(2)/J(1) approximately 12 exceeds the reported value by an order of magnitude. Using geometrical considerations, high temperature expansions and perturbative mean field theory, we show that the LDA-derived exchange constants lead to a remarkably accurate description of the properties of these materials including specific heat, susceptibility, Néel temperature, and NMR spectra.

Two-dimensional randomly frustrated spin-1/2 Heisenberg model.

We investigate the properties of S = 1/2 Heisenberg clusters with random frustration using exact diagonalizations. This is a model for a quantum spin glass. We show that the average ground state spin is S proportional to the square root of N, where N is the number of sites. We also calculate the magnetic susceptibility and the spin stiffness and low-energy excitations and discuss these in terms of a semiclassical picture.