We investigate the half-filled Hubbard model on an isotropic triangular lattice with the variational cluster approximation. By decreasing the on-site repulsion U (or equivalently increasing pressure) we go from a phase with long range, three-sublattice, spiral magnetic order, to a non-magnetic Mott insulating phase -a spin liquid -and then, for U 6.7t, to a metallic phase. Clusters of sizes 3, 6 and 15 with open boundary conditions are used in these calculations, and an extrapolation to infinite size is argued to lead to a disordered phase at U = 8t, but to a spiral order at U 12.The effect of geometric frustration on quantum magnetism is still a very active field of investigation. The quantum Heisenberg model on a two-dimensional square (bipartite) lattice exhibits long-range Néel order, but that order is suppressed on an isotropic triangular lattice. In that case, the classical ground state is a spiral configuration in which the magnetization on each of the three sub-lattices is oriented at 120• of the other two. For a while, it was conjectured that quantum fluctuations around that classical ground state would be strong enough to destroy this ordered pattern, but there is now a quasi-consensus that this is not the case However, real antiferromagnets are better described by the Hubbard model,where t is the hopping amplitude between neighboring sites, c iσ destroys an electron of spin σ at site i and U is the on-site Coulomb repulsion. The Heisenberg model is recovered in the strong coupling limit (U t), with direct-exchange constant J ∼ 4t 2 /U . Finite-U effects are potentially important on real systems to which the Heisenberg model is usually applied. Such effects are often incorporated as ring-exchange terms in spin models [3], but their origin can be traced back to the Hubbard model itself [4]. For instance, the organic conductor κ-(BEDT-TTF) 2 Cu 2 (CN) 3 may be described by a Hubbard model on an almost isotropic and half-filled triangular lattice [5], and this material is conjectured to be in a spin liquid (i.e. magnetically disordered and insulating) phase [6]. So is the triangular antiferromagnet EtMe 3 Sb[Pd(dmit) 2 ] 2 [7]. The question that arises in this case is whether such a state is compatible with a Hubbard model description. In this paper, we will argue that it is, i.e., that the Hubbard model on a triangular lattice exhibits a spin liquid phase at intermediate values of U (e.g. U ∼ 8) although it exhibits spiral magnetic order at stronger coupling (e.g. at U = 12). The Hubbard model on an anisotropic triangular lattice has been studied by various methods. The 120• spiral state has been studied in the mean-field approximation [8,9], and a spin stiffness analysis points to a loss of order for U 6 [9]. In the isotropic case, slave-bosons methods were used to obtain a phase diagram qualitatively similar to the Hartree-Fock results [10], with a transition from a metallic phase to a magnetic phase, with no intercalated spin liquid phase. On the other hand, the presence of a Mott phase was confirmed ...

The κ-(ET)2X layered conductors (where ET stands for BEDT-TTF) are studied within the dimer model as a function of the diagonal hopping t ′ and Hubbard repulsion U . Antiferromagnetism and d-wave superconductivity are investigated at zero temperature using variational cluster perturbation theory (V-CPT). For large U , Néel antiferromagnetism exists for t ′ < t ′ c2 , with t ′ c2 ∼ 0.9. For fixed t ′ , as U is decreased (or pressure increased), a d x 2 −y 2 superconducting phase appears. When U is decreased further, the a dxy order takes over. There is a critical value of t ′ c1 ∼ 0.8 of t ′ beyond which the AF and dSC phases are separated by Mott disordered phase.The proximity of antiferromagnetism (AF) and d-wave superconductivity (dSC) is a central and universal feature of high-temperature superconductors, and leads naturally to the hypothesis that the mechanisms behind the two phases are intimately related. This proximity is also observed in the layered organic conductor κ-(ET) 2 Cu-[N(CN) 2 ]Cl, an antiferromagnet that transits to a superconducting phase upon applying pressure[1] (here ET stands for BEDT-TTF). Other compounds of the same family, κ-(ET) 2 Cu(NCS) 2 and κ-(ET) 2 Cu[N(CN) 2 ]Br, are superconductors with a critical temperature near 10K at ambient pressure. However, another member of this family, κ-(ET) 2 Cu 2 (CN) 3 , displays no sign of AF order, but becomes superconducting upon applying pressure [2,3]. The character of the superconductivity in these compounds is still controversial. While many experiments indicate that the SC gap has nodes (presumably d-wave), others are interpreted as favoring a nodeless gap. The literature on the subject is rich, and we refer to a recent review article[4] for references.The interplay of AF and dSC orders, common to both high-T c and κ-ET materials, cannot be fortuitous and must be a robust feature that can be captured in a simple model of these strongly correlated systems. κ-ET compounds consist of orthogonally aligned ET dimers that form conducting layers sandwiched between insulating polymerized anion layers. The simplest theoretical description of these complex compounds is the so-called dimer Hubbard model [5,6] (Fig. 1A) in which a single bonding orbital is considered on each dimer, occupied by one electron on average, with the Hamiltonianwhere c rσ (c † rσ ) creates an electron (hole) at dimer site r on a square lattice with spin projection σ, and n rσ =c † rσ c rσ is the hole number operator. rr ′ ([rr ′ ]) indicates nearest-(next-nearest)-neighbor bonds. As the ratio t ′ /t grows from 0 towards 1, Néel AF is increasingly

Motivated by the possibility of superconductivity in doped graphene sheets, we investigate superconducting order in the extended Hubbard model on the two-dimensional graphene lattice using the variational cluster approximation (VCA) and the cellular dynamical mean-field theory (CDMFT) with an exact diagonalization solver at zero temperature. The nearest-neighbor interaction is treated using a mean-field decoupling between clusters. We compare different pairing symmetries, singlet and triplet, based on short-range pairing. VCA simulations show that the real (nonchiral), triplet p-wave symmetry is favored for small V , small on-site interaction U or large doping, whereas the chiral combination p + ip is favored for larger values of V , stronger on-site interaction U or smaller doping. CDMFT simulations confirm the stability of the p + ip solution, even at half-filling. Singlet superconductivity (extended s-wave or d-wave) is either absent or sub-dominant.