146 research outputs found
The charge and spin sectors of the - Hubbard model
The charge and spin sectors, which are intimately coupled to the fermionic
one, of the - 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 - 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
-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
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
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
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
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