We present results on the entropy and heat capacity of spin-S honeycomb-lattice Kitaev models using high-temperature series expansions and thermal pure quantum state methods. We study models with anisotropic couplings Jz=1≥Jx=Jy for spin values 1/2, 1, 3/2, and 2. We show that for S>1/2, any anisotropy leads to well-developed plateaus in the entropy function at an entropy value of 12ln2, independent of S. However, in the absence of anisotropy, there is an incipient entropy plateau at Smax/2, where Smax is the infinite temperature entropy of the system. We discuss the possible underlying microscopic reasons for the origin and implications of these entropy plateaus.

Motivated by the geometry of spins in the materials SrCu2O3 and CaCu2O3, we study a two-layer, spin-half Heisenberg model, with nearest-neighbor exchange couplings J and alphaJ along the two axes in the plane and a coupling J(perpendicular to) perpendicular to the planes. We study these class of models using the stochastic series expansion quantum Monte Carlo simulations at finite temperatures and series expansion methods at T=0. The critical value of the interlayer coupling, J(perpendicular to)(c), separating the Neel ordered and disordered ground states, is found to follow very closely a square root dependence on alpha. Both T=0 and finite-temperature properties of the model are presented and the contrasting behavior of SrCu2O3 and CaCu2O3 are explained.

We consider a lattice model of itinerant electrons coupled to an array of localized classical Heisenberg spins. The nature of the ground-state-ordered magnetic phases that result from the indirect spin-spin coupling mediated by the electrons is determined as a function of density and the spin-fermion coupling J. At a fixed chemical potential, spiral phases exist only up to values of J which are less than roughly half the electronic bandwidth. At a fixed electron density and near half filling, the system phase-separates into a half-filled antiferromagnetic phase and a spiral phase. The ferromagnetic phases are shown to be fully polarized, while the spiral phases have equal admixture of up and down spins. Phase separation survives in the presence of weak pairing field Δ but disappears when Δ exceeds a critical value Δc. If pairing fields are large enough, an additional spiral state arises at strong coupling J. The relevance of this study, especially the phase separation, to artificially engineered systems of adjacent itinerant electrons and localized spins is discussed. In particular, we propose a method which might allow for the braiding of Majorana fermions by changing the density and moving their location as they are pulled along by a phase separation boundary.

We use numerical linked cluster expansions (NLC) and exact diagonalization to study confinement transitions out of the quantum spin liquid phase in the pyrochlore-lattice Ising antiferromagnet with random transverse fields. We calculate entanglement entropies associated with local regions defined by single tetrahedron to observe these transitions. The randomness-induced confinement transition is marked by a sharp reduction in the local entanglement and a concomitant increase in Ising correlations. In NLC, it is studied through the destruction of loop resonances due to random transverse-fields. The confining phase is characterized by a distribution of local entanglement entropies, which persists to large random fields.

The pairing symmetry of interacting Dirac fermions on the π-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The s∗- (i.e., extended s-) and d-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional ds∗-wave phase consisting of alternating stripes of s∗- and d-wave phases. A complementary mean-field analysis shows that while the s∗- and d-wave symmetries individually have nodes in the energy spectrum, the ds∗ channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral d-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.