Abstract:
Motivated by recent Quantum Monte Carlo (QMC) simulations of the Quantum Kagome Ice model by Juan Carrasquilla, {\it et al.}, Nature Communications, {\bf 6}, 7421, (2015), we study the ground state phase diagram of this model on the triangular lattice. We show that quantum fluctuations are suppressed in this model, hence the semiclassical approximation is suitable for describing the quantum properties of the system. We uncover the complete quantum phase diagram of this model and show how each phase is markedly different from the well-studied hard-core boson model.

Abstract:
An antiferromagnetic ordering in Pb3TeCo3V2O14 takes place through formation of short range correlation regime with T* ~ 10.5 K and succession of second order phase transition at TN1 = 8.9 K and first order phase transition at TN2 = 6.3 K. An external magnetic field rapidly destroys magnetic structure at T < TN2 and influences the magnetic order at TN2 < T < TN1 resulting in complex magnetic phase diagram of Pb3TeCo3V2O14 as derived from magnetization and specific heat measurements. The first principles calculations indicate that in variance with layered crystal structure the magnetic subsystem of Pb3TeCo3V2O14 is quasi-one-dimensional and highly unusual consisting of weakly coupled triangular tubes.

Abstract:
We investigate the Hubbard model on the anisotropic triangular lattice as a suggested effective description of the Mott phase in various triangular organic compounds. Employing the variational cluster approximation and the ladder dual-fermion approach as complementary methods to adequately treat the zero-temperature and the finite-temperature domains, we obtain a consistent picture of the phase diagram as a function of anisotropy and interaction strength. The metal-insulator transition substantially depends on the anisotropy, and so does the nature of magnetism and the emergence of a nonmagnetic insulating phase. We further find that geometric anisotropy significantly influences the thermodynamics of the system. For increased frustration induced by anisotropy, the entropy of the system increases with interaction strength, opening the possibility of adiabatically cooling a frustrated system by an enhancement of electronic correlations.

Abstract:
Using magnetic torque measurement on a NaNiO2 single crystal, we have established the magnetic phase diagram of this triangular compound. It presents 5 different phases depending on the temperature (4 K - 300 K) and magnetic field (0 - 22 T) revealing several spin reorientations coupled to different magnetic anisotropies.

Abstract:
We determine the quantum phase diagram of the antiferromagnetic spin-1/2 XXZ model on the triangular lattice as a function of magnetic field and anisotropic coupling $J_z$. Using the density matrix renormalization group (DMRG) algorithm in two dimensions we establish the locations of the phase boundaries between a plateau phase with 1/3 N\'eel order and two distinct coplanar phases. The two coplanar phases are characterized by a simultaneous breaking of both translational and U(1) symmetries, which is reminiscent of supersolidity. A translationally invariant umbrella phase is entered via a first order phase transition at relatively small values of $J_z$ compared to the corresponding case of ferromagnetic hopping and the classical model. The phase transition lines meet at two tricritical points on the tip of the lobe of the plateau state, so that the two coplanar states are completely disconnected. Interestingly, the phase transition between the plateau state and the upper coplanar state changes from second order to first order for large values of $J_z > 2.5J$.

Abstract:
We study the electronic states of the anisotropic triangular lattice Hubbard model at half filling, which is a simple effective model for the organic superconducting $\kappa$-BEDT-TTF compounds. We treat the effect of the Coulomb interaction by the fluctuation exchange (FLEX) method, and obtain the phase diagram of this model for various sets of parameters. It is shown that the d-wave superconductivity is realized in the wide region of the phase diagram, next to the antiferromagnetic states. The obtained phase diagram explains the characters of the experimental results very well.

Abstract:
We present selfdual manifolds for coupled Potts models on the triangular lattice. We exploit two different techniques: duality followed by decimation, and mapping to a related loop model. The latter technique is found to be superior, and it allows to include three-spin couplings. Starting from three coupled models, such couplings are necessary for generating selfdual solutions. A numerical study of the case of two coupled models leads to the identification of novel critical points.

Abstract:
We study the spin-half Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square-lattice at one end, a set of decoupled spin-chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations and varying dimensionality. There is a large region of the usual 2-sublattice Ne\'el phase, a 3-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wavevector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical.

Abstract:
The 2-leg t-J ladder forms a spin liquid at half-filling which evolves to a Luther-Emery liquid upon doping. Our aim is to obtain a complete phase diagram for isotropic coupling (i.e. rungs and legs equal) as a function of electron density n and the ratio J/t (>0). Two known limiting cases are: n<1/2 which is a single band Luttinger liquid and small hole doping for J/t close to 0 which is a Nagaoka ferromagnet. Using Lanczos techniques we examine the region between the Nagaoka and Luther-Emery phases for 1>n>1/2. We find evidences for gapless behavior in both spin and charge channels for J/t<0.3 consistent with Luttinger liquids in both bonding and anti-bonding bands (i.e., C2S2). This proposal is based on the behavior of spin and charge correlation functions. For example the hole-hole correlation function which displays hole pairing at larger J/t, shows hole-hole repulsion in this region. As a further test, we examined the dependence of the energy on a relative phase shift between bonding and antibonding bands. For J/t < 0.3 this is very weak, indicating a lack of pairing between these channels.

Abstract:
We study the extended Hubbard model on the triangular lattice as a function of filling and interaction strength. The complex interplay of kinetic frustration and strong interactions on the triangular lattice leads to exotic phases where long-range charge order, antiferromagnetic order, and metallic conductivity can coexist. Variational Monte Carlo simulations show that three kinds of ordered metallic states are stable as a function of nearest neighbor interaction and filling. The coexistence of conductivity and order is explained by a separation into two functional classes of particles: part of them contributes to the stable order, while the other part forms a partially filled band on the remaining substructure. The relation to charge ordering in charge transfer salts is discussed.