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We consider the low-energy region of an array of Luttinger liquids coupled by a weak interchain hopping. The leading logarithmic divergences can be re-summed to all orders within a self-consistent perturbative expansion in the hopping, in the large-dimension limit. The anomalous exponent scales to zero below the one-particle crossover temperature. As a consequence, coherent quasiparticles with finite weight appear along the whole Fermi surface. Extending the expansion self-consistently to all...
We study the spin and charge phase diagram of a three-legs ladder (at zero temperature) as a function of fermion density and of transverse single-particle hopping by means of a Renormalization-Group analysis rigorously controlled in the weak-coupling limit. Periodic boundary conditions in the direction transverse to the ladder produce frustrated magnetic excitations yielding a spin-gapped phase in a large region about and at half filling. Spin correlations are instead enhanced when open trans...
We analyze the problem of Luttinger liquids coupled via a single-particle hopping $\tp$ and introduce a systematic diagrammatic expansion in powers of $\tp$. An analysis of the scaling of the diagrams at each order allows us to determine the power-law behavior versus $\tp$ of the interchain hopping and of the Fermi surface warp. In particular, for strong interactions, we find that the exponents are dominated by higher-order diagrams producing an enhanced coherence and a failure of linear-resp...
We carry out a theoretical study of the bilayer single-band Hubbard model in the undoped and in the superconducting phases by means of the variational cluster approach. In particular, we focus on the splitting between the ?bonding? and ?antibonding? bands induced by the interlayer hopping, as well as its interplay with strong correlation effects. We find that the splitting is considerably suppressed in both the normal and superconducting phases, in qualitative agreement with experiments on Bi...
Recent angle resolved photoemission data, which found evidence for a d-wave-like modulation of the antiferromagnetic gap, suggest an intimate interrelation between the antiferromagnetic insulator and the superconductor with its d-wave gap. It is shown here that a projected SO(5) theory, which explicitly takes the Mott-Hubbard gap into account, correctly describes the observed gap characteristics. Specifically, it accounts for the order of magnitude difference between the antiferromagnetic gap...
We examine the competition and relationship between an antiferromagnetic (AF) Mott insulating state and a d_{x^2-y^2} superconducting (SC) state in two dimensions using semi-analytical, i. e. diagrammatic calculations of the t-U-W model. The AF Mott insulator is described by the ground state of the half-filled Hubbard model on a square lattice with on-site Coulomb repulsion U and nearest neighbor single-particle hopping t. To this model, an extra term W is added, which depends upon the square...
Spectral excitations of ultracold gases of bosonic atoms trapped in one dimensional optical lattices with disorder are investigated by means of the variational cluster approach applied to the Bose-Hubbard model. In particular, qualitatively different disorder distributions typically employed in experiments are considered. The computed spectra exhibit a strong dependence on both the shape of the disorder distribution and the disorder strength. We compare alternative results for the Mott gap ob...
We present improvements of a recently introduced numerical method [Arrigoni etal, Phys. Rev. Lett. 110, 086403 (2013)] to compute steady state properties of strongly correlated electronic systems out of equilibrium. The method can be considered as a non-equilibrium generalization of exact diagonalization based dynamical mean-field theory (DMFT). The key modification for the non-equilibrium situation consists in addressing the DMFT impurity problem within an auxiliary system consisting of the ...