Ferdinando Mancini

Doping dependence of on-site quantities in the two-dimensional Hubbard model

Abstract The two-dimensional Hubbard model is studied by means of the composite operator approach. In a generalized mean-field approximation we calculate local quantities, as the double occupancy and the magnetic moment, for various values of the particle density, repulsive Coulomb interaction and temperature. Comparison with the results obtained by other authors by means of numerical analysis shows quite good agreement.

Spin magnetic susceptibility in the two-dimensional Hubbard model

Abstract The spin magnetic susceptibility for the two-dimensional one-band Hubbard model is calculated by means of the composite operator method. The results agree with data obtained by means of numerical analysis and qualitatively reproduce some of the unusual magnetic properties observed in the normal state of high- T c superconducting materials.

Equation of Motion Method for Composite Field Operators

Abstract.The Green’s function formalism in Condensed Matter Physics is reviewed within the equation of motion approach. Composite operators and their Green’s functions naturally appear as building blocks of generalized perturbative approaches and require fully self-consistent treatments in order to be properly handled. It is shown how to unambiguously set the representation of the Hilbert space by fixing both the unknown parameters, which appear in the linearized equations of motion and in the spectral weights of non-canonical operators, and the zero-frequency components of Green’s functions in a way that algebra and symmetries are preserved. To illustrate this procedure some examples are given: the complete solution of the two-site Hubbard model, the evaluation of spin and charge correlators for a narrow-band Bloch system, the complete solution of the three-site Heisenberg model, and a study of the spin dynamics in the Double-Exchange model.

THE HUBBARD MODEL IN THE TWO-POLE APPROXIMATION

The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying the conservation of the first four spectral momenta. It emerges that the various methods differ only in the way of fixing the internal parameters and that it exists a unique way to preserve simultaneously the Pauli principle and the particle–hole symmetry. A comprehensive comparison with respect to some general symmetry properties and the data from quantum Monte Carlo analysis shows the relevance of imposing the Pauli principle.

Energy and chemical potential in the two-dimensional Hubbard model

The two-dimensional Hubbard model is studied by means of the composite-operator approach. In a generalized mean-field approximation we calculate the ground-state energy and the chemical potential, for various values of the particle density, repulsive Coulomb interaction and temperature. Comparison with the results obtained by other authors by means of numerical analysis shows a good agreement.

Strongly Correlated Systems

Self-energy-functional theory is a formal framework which allows to derive non-perturbative and thermodynamically consistent approximations for lattice models of strongly correlated electrons from a general dynamical variational principle. The construction of the self-energy functional and the corresponding variational principle is developed within the path-integral formalism. Different cluster mean-field approximations, like the variational cluster approximation and cluster extensions of dynamical mean-field theory are derived in this context and their mutual relationship and internal consistency are discussed.Pseudoparticle Approach. - Functional Renormalization Group (FunRG). - Projection Operator Method. - Composite Operator Method (COM). - LDA+GTB method. - Dynamical Mean-Field Theory (DMFT). - Cluster Perturbation Theory (CPT). - Self-Energy-Functional Theory (SFA). - Cluster Dynamical Mean Field Theory (CDMFT). - Dynamical Cluster Approximation (DCA). - Density Functional Theory (DFT). - Gutzwiller, Slave Boson and RVB. - Two-Particle-Self-Consistent Approach (TPSC).

Bosonic sector of the two-dimensional Hubbard model studied within a two-pole approximation

The charge and spin dynamics of the two-dimensional Hubbard model in the paramagnetic phase is first studied by means of the two-pole approximation within the framework of the composite operator method. The fully self-consistent scheme requires: no decoupling, the fulfillment of both Pauli principle and hydrodynamic constraints, the simultaneous solution of fermionic and bosonic sectors, and a very rich momentum dependence of the response functions. The temperature and momentum dependencies, as well as the dependency on the Coulomb repulsion strength and the filling, of the calculated charge and spin susceptibilities and correlation functions are in very good agreement with the numerical calculations present in the literature.

The superconducting gap in the two-dimensional Hubbard model

Abstract Superconductivity with singlet d -wave pairing has been studied for the two-dimensional single-band Hubbard model by means of the composite operator method. Results are given for the one-particle energy gap as a function of wave vector.

Underdoped cuprate phenomenology in the two-dimensional Hubbard model within the composite operator method

The two-dimensional Hubbard model is studied within the Composite Operator Method (COM) with the residual self-energy computed in the Self-Consistent Born Approximation (SCBA). COM describes interacting electrons in terms of the new elementary excitations appearing in the system owing to strong correlations; residual interactions among these excitations are treated within the SCBA. The anomalous features appearing in the spectral function A(k,\omega), the momentum distribution function n(k) and the Fermi surface are analyzed for various values of the filling (from overdoped to underdoped region) in the intermediate coupling regime at low temperatures. For low doping, in contrast with the ordinary Fermi-liquid behavior of a weakly-correlated metal found at high doping, we report the opening of a pseudogap and some non-Fermi-liquid features as measured for cuprates superconductors. In addition, we show the presence of kinks in the calculated electronic dispersion in agreement with ARPES data.

Antiferromagnetic phase in the Hubbard model by means of the composite operator method

We have investigated the antiferromagnetic phase of two-dimensional (2D), three-dimensional (3D), and extended Hubbard models on a bipartite cubic lattice by means of the composite operator method within a two-pole approximation. This approach yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of both the model and the algebra. The complete phase diagram, as regards the antiferromagnetic and paramagnetic phases, has been drawn. We first reported, within a pole approximation, three kinds of transitions at half-filling: Mott-Hubbard, Mott-Heisenberg, and Heisenberg transitions. We have also found a metal-insulator transition, driven by doping, within the antiferromagnetic phase. This latter is restricted to a very small region near half-filling, and has, in contrast to what has been found by similar approaches, a finite critical Coulomb interaction as a lower bound at half-filling. Finally, it is worth noting that our antiferromagnetic gap has two independent components: one due to the antiferromagnetic correlations, and another coming from the Mott-Hubbard mechanism.