Abstract:
The temporal magnetic correlations of the triangular lattice antiferromagnet NiGa$_2$S$_4$ are examined through thirteen decades ($10^{-13}-1$~sec) using ultra-high-resolution inelastic neutron scattering, muon spin relaxation, AC and nonlinear susceptibility measurements. Unlike the short-ranged {\it spatial} correlations, the temperature dependence of the {\it temporal} correlations show distinct anomalies. The spin fluctuation rate decreases precipitously upon cooling towards $T^{\ast}=8.5$~K, but fluctuations on the microsecond time scale then persist in an anomalous dynamical regime for 4 K $

Abstract:
We apply the coupled cluster method and exact diagonalzation to study the uniform susceptibility and the ground-state magnetization curve of the triangular-lattice spin-1 Heisenberg antiferromagnet. Comparing our theoretical data for the magnetization curve with recent measurements on the s=1 triangular lattice antiferromagnet Ba3NiSb2O9 we find a very good agreement.

Abstract:
We investigate the anisotropic triangular lattice that interpolates from decoupled one-dimensional chains to the isotropic triangular lattice and has been suggested to be relevant for various quasi-two-dimensional materials, such as Cs$_2$CuCl$_4$ or $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$, an organic material that shows intriguing magnetic properties. We obtain an excellent accuracy by means of a novel representation for the resonating valence bond wave function with both singlet and triplet pairing. This approach allows us to establish that the magnetic order is rapidly destroyed away from the pure triangular lattice and incommensurate spin correlations are short range. A non-magnetic spin liquid naturally emerges in a wide range of the phase diagram, with strong one-dimensional character. The relevance of the triplet pairing for $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$ is also discussed.

Abstract:
In order to clarify whether the odd-frequency superconductivity can be realized or not, we study a quasi-one-dimensional triangular lattice in the Hubbard model using the random phase approximation (RPA) and the fluctuation exchange (FLEX) approximation. We find that odd-frequency spin-singlet p-wave pairing can be enhanced on a quasi-one-dimensional isosceles triangular lattice.

Abstract:
Spin scalar chiral ordering gives rise to nontrivial topological characters and peculiar transport properties. We here examine how quantum spin fluctuations affect the spin scalar chiral ordering in itinerant electron systems. We take the Kondo lattice model on a triangular lattice, and perform the linear spin wave analysis in the Chern insulator phases with spin scalar chiral ordering obtained in the case that the localized spins are classical. We find that, although the quantum fluctuation destabilizes the spin scalar chiral phase at 3/4 filling that originates from the perfect nesting of Fermi surface, it retains the phase at 1/4 filling that is induced by an effective positive biquadratic interaction. The reduction of the ordered magnetic moment by the zero-point quantum fluctuation is considerably small, compared with those in spin-only systems. The results suggest that the Chern insulator at 1/4 filling remains robust under quantum fluctuations.

Abstract:
We study ring-exchange models for bosons or XY-spins on the triangular lattice. A four-spin exchange leads to a manifold of ground states with gapless excitations and critical power-law correlations. With a nearest-neighbour exchange, fluctuations select a four-fold ferrimagnetically ordered ground state with a small spin/superfluid stiffness which breaks the global U(1) and translational symmetry. We explore consequences for phase transitions at finite temperature and in an in-plane magnetic field.

Abstract:
We study the spin-1/2 Heisenberg model in a lattice that interpolates between the triangular and the kagome lattices. The exchange interaction along the bonds of the kagome lattice is J, and the one along the bonds connecting kagome and non-kagome sites is J', so that J'=J corresponds to the triangular limit and J'=0 to the kagome one. We use variational and exact diagonalization techniques. We analyze the behavior of the order parameter for the antiferromagnetic phase of the triangular lattice, the spin gap, and the structure of the spin excitations as functions of J'/J. Our results indicate that the antiferromagnetic order is not affected by the reduction of J' down to J'/J ~ 0.2. Below this value, antiferromagnetic correlations grow weaker, a description of the ground state in terms of a Neel phase renormalized by quantum fluctuations becomes inadequate, and the finite-size spectra develop features that are not compatible with antiferromagnetic ordering. However, this phase does not appear to be connected to the kagome phase as well, as the low-energy spectra do not evolve with continuity for J'-> 0 to the kagome limit. In particular, for any non-zero value of J', the latter interaction sets the energy scale for the low-lying spin excitations, and a gapless triplet spectrum, destabilizing the kagome phase, is expected.

Abstract:
A linear spin-wave approach, a variational method and exact diagonlization are used to investigate the magnetic long-range order (LRO) of the spin-1/2 Heisenberg antiferromagnet on a two-dimensional 1/7-depleted triangular (maple leaf) lattice consisting of triangles and hexagons only. This lattice has z=5 nearest neighbors and its coordination number z is therefore between those of the triangular (z=6) and the kagome (z=4) lattices. Calculating spin-spin correlations, sublattice magnetization, spin stiffness, spin-wave velocity and spin gap we find that the classical 6-sublattice LRO is strongly renormalized by quantum fluctuations, however, remains stable also in the quantum model.

Abstract:
We investigate the Hubbard model on the anisotropic triangular lattice with two hopping parameters $t$ and $t^\prime$ in different spatial directions, interpolating between decoupled chains ($t=0$) and the isotropic triangular lattice ($t=t^\prime$). Variational wave functions that include both Jastrow and backflow terms are used to compare spin-liquid and magnetic phases with different pitch vectors describing both collinear and coplanar (spiral) order. For relatively large values of the on-site interaction $U/t^\prime \gtrsim 10$ and substantial frustration, i.e., $0.3\lesssim t/t^\prime \lesssim 0.8$, the spin-liquid state is clearly favored over magnetic states. Spiral magnetic order is only stable in the vicinity of the isotropic point, while collinear order is obtained in a wide range of inter-chain hoppings from small to intermediate frustration.

Abstract:
We study the triangular lattice Ising model with a finite number of vertically stacked layers and demonstrate a low temperature reentrance of two Berezinskii-Kosterlitz-Thouless transitions, which results in an extended disordered regime down to $T=0$. Numerical results are complemented with the derivation of an effective low-temperature dimer theory. Contrary to order by disorder, we present a new scenario for fluctuation-induced ordering in frustrated spin systems. While short-range spin-spin correlations are enhanced by fluctuations, quasi-long-range ordering is precluded at low enough temperatures by proliferation of topological defects.