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.

We study the spinful fermionic Haldane-Hubbard model at half filling using a combination of quantum cluster methods: cluster perturbation theory (CPT), the variational cluster approximation (VCA), and cluster dynamical mean-field theory (CDMFT). We explore possible zero-temperature phases of the model as a function of on-site repulsive interaction strength and next-nearest-neighbor hopping amplitude and phase. Our approach allows us to access the regime of intermediate interaction strength, where charge fluctuations are significant and effective spin model descriptions may not be justified. Our approach also improves upon mean-field solutions of the Haldane-Hubbard model by retaining local quantum fluctuations and treating them nonperturbatively. We find a correlated topological Chern insulator for weak interactions and a topologically trivial Néel antiferromagnetic insulator for strong interactions. For intermediate interactions, we find that topologically nontrivial Néel antiferromagnetic insulating phases and/or a topologically nontrivial nonmagnetic insulating phase may be stabilized.

The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at strong coupling, interpolates between the Heisenberg model and the Kitaev model. It is basically a Hubbard model with ordinary hopping t and spin-dependent hopping t . We study this model in the weak to intermediate coupling regime, at half-filling, using the Cellular Dynamical Impurity Approximation (CDIA), an approach related to Dynamical Mean Field Theory but based on Potthoff's variational principle. We identify four phases in the (U, t ) plane: two semi-metallic phases with different numbers of Dirac points, an antiferromagnetic insulator, and an algebraic spin liquid. The last two are separated by a first-order transition. These four phases all meet at a single point and could be realized in cold atom systems. arXiv:1506.00501v1 [cond-mat.str-el] 1 Jun 2015

It is now well established that superconducting cuprates support a charge density wave state in the socalled underdoped region of their phase diagram. We investigate the possibility of charge order in the square-lattice Hubbard model, both alone and in coexistence with d-wave superconductivity. The charge order has a period four in one direction, is centered on bonds and has a d form factor. We use the variational cluster approximation, an approach based on a rigorous variational principle that treats shortrange correlations exactly, with two clusters of size 2 × 6 that together tile the infinite lattice and provide a non-biased unit for a period-four bond density wave (BDW). We find that the BDW exists in a finite range of hole doping and increases in strength from U = 5 to U = 8. Its location and intensity depends strongly on the band dispersion. When probed simultaneously with d-wave superconductivity, the energy is sometimes lowered by the presence of both phases, depending on the interaction strength. Whenever they coexist, a pair-density wave (a modulation of superconducting pairing with the same period and form factor as the BDW) also exists.

We investigate superconducting order in the extended Hubbard model on the two-dimensional graphene lattice using the variational cluster approximation (VCA) with an exact diagonalization solver at zero temperature. Building on the results of Ref.[1], which identified triplet p-and p + ip-wave superconductivity as the most favored pairing symmetries in that model, we place uniform SC solutions in competition with a nonuniform Kekulé (p+i p-K) superconducting pattern, similar to those proposed in Ref. [2]. We find that the p+i p-K solution is in fact the most favored pairing in most of the phase diagram. In addition, we show that antiferromagnetism can co-exist with the p+ip-K state and that both orders are enhanced by their coexistence.

We study the one-band Hubbard model on the trellis lattice, a two-dimensional frustrated lattice of coupled two-leg ladders, with hopping amplitude t within ladders and t between ladders. For large U/t this is a model for the cuprate Sr14−xCaxCu24O41. We investigate the phase diagram as a function of doping for U = 10t using two quantum cluster methods: The variational cluster approximation (VCA), with clusters of sizes 8 and 12, and Cellular dynamical mean field theory (CDMFT), both at zero temperature. Both methods predict a superconducting dome, ending at roughly 20% doping in VCA and 15% in CDMFT. In VCA, the superconducting order parameter is complex in a range of doping centered around 10%, corresponding to bulk chiral, T -violating superconductivity. However, the CDMFT solution is not chiral. We find evidence for a migration of the Cooper pairs from the inter-ladder region towards the plaquettes as doping is increased.

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The interplay between the Kondo effect and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida interaction is studied within the two-dimensional Hubbard-Kondo lattice model. In addition to the antiferromagnetic exchange interaction, J ⊥ , between the localized and the conduction electrons, this model also contains the local repulsion, U, between the conduction electrons. We use variational cluster approximation to investigate the competition between the antiferromagnetic phase, the Kondo singlet phase, and a ferrimagnetic phase on square lattice. At half-filling, the Néel antiferromagnetic phase dominates from small to moderate J ⊥ and UJ ⊥ , and the Kondo singlet elsewhere. Sufficiently away from half-filling, the antiferromagnetic phase first gives way to a ferrimagnetic phase (in which the localized spins order ferromagnetically, and the conduction electrons do likewise, but the two mutually align antiferromagnetically), and then to the Kondo singlet phase. arXiv:1804.00917v1 [cond-mat.str-el]