On the Analyticity of Solutions in the Dynamical Mean-Field Theory

The unphysical solutions of the periodic Anderson model obtained by H. Keiter and T. Leuders [Europhys. Lett. 49, 801(2000)] in dynamical mean-field theory (DMFT) are shown to result from the author's restricted choice of the functional form of the solution, leading to a violation of the analytic properties of the exact solution. By contrast, iterative solutions of the self-consistency condition within the DMFT obtained by techniques which preserve the correct analytic properties of the exact solution (e.g., quantum Monte-Carlo simulations or the numerical renormalization group) always lead to physical solutions.Comment: 4 pages, 1 figur

Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model

We analyze the competition between antiferromagnetism and superconductivity in the two-dimensional Hubbard model by combining a functional renormalization group flow with a mean-field theory for spontaneous symmetry breaking. Effective interactions are computed by integrating out states above a scale Lambda_{MF} in one-loop approximation, which captures in particular the generation of an attraction in the d-wave Cooper channel from fluctuations in the particle-hole channel. These effective interactions are then used as an input for a mean-field treatment of the remaining low-energy states, with antiferromagnetism, singlet superconductivity and triplet pi-pairing as the possible order parameters. Antiferromagnetism and superconductivity suppress each other, leaving only a small region in parameter space where both orders can coexist with a sizable order parameter for each. Triplet pi-pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small.Comment: 28 pages, 14 figure

Running coupling constants of the Luttinger liquid

Two running coupling constants of the Luttinger liquid are computed in the fermion-fermion and fermion-antifermion channels. Nontrivial scaling laws are found together with Landau poles. The apparent contradiction with the expected vanishing of the beta functions is explained.Comment: Final version, to appear in Phys. Lett.

Correlated hopping of electrons: Effect on the Brinkman-Rice transition and the stability of metallic ferromagnetism

We study the Hubbard model with bond-charge interaction (`correlated hopping') in terms of the Gutzwiller wave function. We show how to express the Gutzwiller expectation value of the bond-charge interaction in terms of the correlated momentum-space occupation. This relation is valid in all spatial dimensions. We find that in infinite dimensions, where the Gutzwiller approximation becomes exact, the bond-charge interaction lowers the critical Hubbard interaction for the Brinkman-Rice metal-insulator transition. The bond-charge interaction also favors ferromagnetic transitions, especially if the density of states is not symmetric and has a large spectral weight below the Fermi energy.Comment: 5 pages, 3 figures; minor changes, published versio

Pseudogap at hot spots in the two-dimensional Hubbard model at weak coupling

We analyze the interaction-induced renormalization of single-particle excitations in the two-dimensional Hubbard model at weak coupling using the Wick-ordered version of the functional renormalization group. The self energy is computed for real frequencies by integrating a flow equation with renormalized two-particle interactions. In the vicinity of hot spots, that is points where the Fermi surface intersects the umklapp surface, self energy effects beyond the usual quasi-particle renormalizations and damping occur near instabilities of the normal, metallic phase. Strongly enhanced renormalized interactions between particles at different hot spots generate a pronounced low-energy peak in the imaginary part of the self energy, leading to a pseudogap-like double-peak structure in the spectral function for single-particle excitations.Comment: 14 pages, 7 figure

The Gutzwiller wave function as a disentanglement prescription

The Gutzwiller variational wave function is shown to correspond to a particular disentanglement of the thermal evolution operator, and to be physically consistent only in the temperature range U<<kT<<E_F, the Fermi energy of the non-interacting system. The correspondence is established without using the Gutzwiller approximation. It provides a systematic procedure for extending the ansatz to the strong-coupling regime. This is carried out to infinite order in a dominant class of commutators. The calculation shows that the classical idea of suppressing double occupation is replaced at low temperatures by a quantum RVB-like condition, which involves phases at neighboring sites. Low-energy phenomenologies are discussed in the light of this result.Comment: Final version as accepted in EPJ B, 10 pages, no figure

Exact analytic results for the Gutzwiller wave function with finite magnetization

We present analytic results for ground-state properties of Hubbard-type models in terms of the Gutzwiller variational wave function with non-zero values of the magnetization m. In dimension D=1 approximation-free evaluations are made possible by appropriate canonical transformations and an analysis of Umklapp processes. We calculate the double occupation and the momentum distribution, as well as its discontinuity at the Fermi surface, for arbitrary values of the interaction parameter g, density n, and magnetization m. These quantities determine the expectation value of the one-dimensional Hubbard Hamiltonian for any symmetric, monotonically increasing dispersion epsilon_k. In particular for nearest-neighbor hopping and densities away from half filling the Gutzwiller wave function is found to predict ferromagnetic behavior for sufficiently large interaction U.Comment: REVTeX 4, 32 pages, 8 figure

Crossover from Luttinger- to Fermi-liquid behavior in strongly anisotropic systems in large dimensions

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 orders turns out to be crucial in order to restore the correct Fermi-liquid behavior.Comment: Shortened version to appear in Physical Review Letter

Fermion loops, loop cancellation and density correlations in two dimensional Fermi systems

We derive explicit results for fermion loops with an arbitrary number of density vertices in two dimensions at zero temperature. The 3-loop is an elementary function of the three external momenta and frequencies, and the N-loop can be expressed as a linear combination of 3-loops with coefficients that are rational functions of momenta and frequencies. We show that the divergencies of single loops for low energy and small momenta cancel each other when loops with permuted external variables are summed. The symmetrized N-loop, i.e. the connected N-point density correlation function of the Fermi gas, does not diverge for low energies and small momenta. In the dynamical limit, where momenta scale to zero at fixed finite energy variables, the symmetrized N-loop vanishes as the (2N-2)-th power of the scale parameter.Comment: 24 pages (including 3 EPS figures), LaTeX2e; submitted to Phys. Rev.