The charge and spin sectors of the tt-t′t' Hubbard model

The charge and spin sectors, which are intimately coupled to the fermionic one, of the $t$-$t'$ Hubbard model have been computed self-consistently within the two-pole approximation. The relevant unknown correlators appearing in the causal bosonic propagators have been computed by enforcing the constraints dictated by the hydrodynamics and the algebra of the composite operators coming into play. The proposed scheme of approximation extends previous calculations made for the fermionic sector of the $t$-$t'$ Hubbard model and the bosonic sector of the Hubbard model, which showed to be very effective to describe the overdoped region of cuprates (the former) and the magnetic response of their parent compounds (the latter)

Composite Operator Method analysis of the underdoped cuprates puzzle

The microscopical analysis of the unconventional and puzzling physics of the underdoped cuprates, as carried out lately by means of the Composite Operator Method (COM) applied to the 2D Hubbard model, is reviewed and systematized. The 2D Hubbard model has been adopted as it has been considered the minimal model capable to describe the most peculiar features of cuprates held responsible for their anomalous behavior. COM is designed to endorse, since its foundations, the systematic emergence in any SCS of new elementary excitations described by composite operators obeying non-canonical algebras. In this case (underdoped cuprates - 2D Hubbard model), the residual interactions - beyond a 2-pole approximation - between the new elementary electronic excitations, dictated by the strong local Coulomb repulsion and well described by the two Hubbard composite operators, have been treated within the Non Crossing Approximation. Given this recipe and exploiting the few unknowns to enforce the Pauli principle content in the solution, it is possible to qualitatively describe some of the anomalous features of high-Tc cuprate superconductors such as large vs. small Fermi surface dichotomy, Fermi surface deconstruction (appearance of Fermi arcs), nodal vs. anti-nodal physics, pseudogap(s), kinks in the electronic dispersion. The resulting scenario envisages a smooth crossover between an ordinary weakly-interacting metal sustaining weak, short-range antiferromagnetic correlations in the overdoped regime to an unconventional poor metal characterized by very strong, long-but-finite-range antiferromagnetic correlations leading to momentum-selective non-Fermi liquid features as well as to the opening of a pseudogap and to the striking differences between the nodal and the anti-nodal dynamics in the underdoped regime.Comment: 30 PRB pages, 13 figures, 35 panel

The Hubbard model: bosonic excitations and zero-frequency constants

A fully self-consistent calculation of the bosonic dynamics of the Hubbard model is developed within the Composite Operator Method. From one side we consider a basic set of fermionic composite operators (Hubbard fields) and calculate the retarded propagators. On the other side we consider a basic set of bosonic composite operators (charge, spin and pair) and calculate the causal propagators. The equations for the Green's functions (GF) (retarded and causal), studied in the polar approximation, are coupled and depend on a set of parameters not determined by the dynamics. First, the pair sector is self-consistently solved together with the fermionic one and the zero-frequency constants (ZFC) are calculated not assuming the ergodic value, but fixing the representation of the GF in such a way to maintain the constrains required by the algebra of the composite fields. Then, the scheme to compute the charge and spin sectors, ZFCs included, is given in terms of the fermionic and pair correlators

The Hubbard model beyond the two-pole approximation: a Composite Operator Method study

Within the framework of the Composite Operator Method, a three-pole solution for the two-dimensional Hubbard model is presented and analyzed in detail. In addition to the two Hubbard operators, the operatorial basis comprises a third operator describing electronic transitions dressed by nearest-neighbor spin fluctuations. These latter, compared to charge and pair fluctuations, are assumed to be preeminent in the region of model-parameter space - small doping, low temperature and large on-site Coulomb repulsion - where one expects strong electronic correlations to dominate the physics of the system. This assumption and the consequent choice for the basic field, as well as the whole analytical approximation framework, have been validated through a comprehensive comparison with data for local and single-particle properties obtained by different numerical methods on varying all model parameters. The results systematically agree, both quantitatively and qualitatively, up to coincide in many cases. Many relevant features of the model, reflected by the numerical data, are exactly caught by the proposed solution and, in particular, the crossover between weak and intermediate-strong correlations as well as the shape of the occupied portion of the dispersion. A comprehensive comparison with other $n$-pole solutions is also reported in order to explore and possibly understand the reasons of such good performance.Comment: 19 pages, 8 figures, 27 panel

The Hubbard model with intersite interaction within the Composite Operator Method

We study the one- and two- dimensional extended Hubbard model by means of the Composite Operator Method within the 2-pole approximation. The fermionic propagator is computed fully self-consistently as a function of temperature, filling and Coulomb interactions. The behaviors of the chemical potential (global indicator) and of the double occupancy and nearest-neighbor density- density correlator (local indicators) are analyzed in detail as primary sources of information regarding the instability of the paramagnetic (metal and insulator) phase towards charge ordering driven by the intersite Coulomb interaction. Very rich phase diagrams (multiple first and second order phase transitions, critical points, reentrant behavior) have been found and discussed with respect to both metal-insulator and charge ordering transitions: the connections with the experimental findings relative to some manganese compounds are analyzed. Moreover, the possibility of improving the capability of describing cuprates with respect to the simple Hubbard model is discussed through the analysis of the Fermi surface and density of states features. We also report about the specific heat behavior in presence of the intersite interaction and the appearance of crossing points.Comment: 15 pages, 36 figure

Self-energy-functional theory

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.Comment: chapter in "Theoretical Methods for Strongly Correlated Systems", edited by A. Avella and F. Mancini, Springer (2011), 38 pages, 10 figure

Quantum order by disorder in the Kitaev model on a triangular lattice

We identify and discuss the ground state of a quantum magnet on a triangular lattice with bond-dependent Ising-type spin couplings, that is, a triangular analog of the Kitaev honeycomb model. The classical ground-state manifold of the model is spanned by decoupled Ising-type chains, and its accidental degeneracy is due to the frustrated nature of the anisotropic spin couplings. We show how this subextensive degeneracy is lifted by a quantum order-by-disorder mechanism and study the quantum selection of the ground state by treating short-wavelength fluctuations within the linked cluster expansion and by using the complementary spin-wave theory. We find that quantum fluctuations couple next-nearest-neighbor chains through an emergent four-spin interaction, while nearest-neighbor chains remain decoupled. The remaining discrete degeneracy of the ground state is shown to be protected by a hidden symmetry of the model.Comment: 5 pages, 4 figure

Green's Function Formalism for Highly Correlated Systems

We present the Composite Operator Method (COM) as a modern approach to the study of strongly correlated electronic systems, based on the equation of motion and Green's function method. COM uses propagators of composite operators as building blocks at the basis of approximate calculations and algebra constrains to fix the representation of Green's functions in order to maintain the algebraic and symmetry properties

New Comparisons for Local Quantities of the Two-Dimensional Hubbard Model

We have compared the results of our approximation scheme, the composite operator method, for the double occupancy and the internal energy of the two-dimensional Hubbard model with numerical data obtained by means of the Lanczos and quantum Monte Carlo schemes. The agreement is very good at both half-filling and away from it showing how reliable is the approximation scheme.Comment: 6 pages, 3 figure

Equation of Motion Method for Composite Field Operators

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.Comment: 20 RevTeX4 pages, 4 embedded figure