A theoretical analysis of the thermodynamic response functions of the 2D single{band Hubbard model is carried out by means of the composite operator method.It is shown that all the features of these quantities can be explained by looking at the dependence of the thermodynamic variables on their conjugate ones.In this way, the electronic speci c heat and the entropy per site are determined in the paramagnetic phase.Also, for the electronic speci c heat and internal energy we present two dierent schemes of calculation.It is found that the numerical data from quantum Monte Carlo techniques for the internal energy and electronic speci c heat are well reproduced by determining them through the rst and second temperature derivatives of the chemical potential.The anomalous normal state properties in hole{doped cuprate high Tc superconductors are also well described.Finally, we obtain several characteristic crossing points for the response functions when plotted versus some thermodynamic variables.These peculiar features indicate the existence of more than one energy scale competing with thermal excitations and indicate, as already noted by Vollhardt, a crossover from a non{interacting to a highly correlated behaviour.
A theoretical analysis of the thermodynamic response functions of the 2D single{band Hubbard model is carried out by means of the composite operator method.It is shown that all the features of these quantities can be explained by looking at the dependence of the thermodynamic variables on their conjugate ones.In this way, the electronic speci c heat and the entropy per site are determined in the paramagnetic phase.Also, for the electronic speci c heat and internal energy we present two dierent schemes of calculation.It is found that the numerical data from quantum Monte Carlo techniques for the internal energy and electronic speci c heat are well reproduced by determining them through the rst and second temperature derivatives of the chemical potential.The anomalous normal state properties in hole{doped cuprate high Tc superconductors are also well described.Finally, we obtain several characteristic crossing points for the response functions when plotted versus some thermodynamic variables.These peculiar features indicate the existence of more than one energy scale competing with thermal excitations and indicate, as already noted by Vollhardt, a crossover from a non{interacting to a highly correlated behaviour.
The electronic states of the two-dimensional Hubbard model are investigated by means of a 4-pole approximation within the composite operator method. In addition to the conventional Hubbard operators, we consider other two operators which come from the hierarchy of the equations of motion and carry information regarding nearest-neighbor spin and charge configurations. By means of this operatorial basis, we can study the physics related to the energy scale of J=4t2∕U in addition to the one of U. Present results show relevant physical features, well beyond those previously obtained by means of a 2-pole approximation, such as a four-band structure with shadow bands and a quasiparticle peak at the Fermi level. The Fermi level stays pinned to the band flatness located at $(\ensuremath{\pi},0)$-point within a wide range of hole-doping $(0\ensuremath{\leqslant}\ensuremath{\delta}\ensuremath{\leqslant}0.15)$. A comprehensive analysis of double occupancy, internal energy, specific heat and entropy features have also been performed. All reported results are in excellent agreement with the data of numerical simulations.
We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equations of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameters space. At zero temperature we identify four phases in the plane (U,n) ( U is the on-site potential and n is the filling) and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at T=0 the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit T-->0 of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equations of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.
Strongly correlated electron systems with planar structure, like high{Tc superconductors, are currently under intensive study.In the search for a realistic model to describe the anomalous behaviors of these systems, we have studied the 2D Extended Hubbard model by means of the Composite Operator Method.The local properties, the density of states and the Fermi surface have been calculated as functions of the model parameters.Particular attention has been paid to the role played by the intersite interaction V which drives important changes in the electronic properties of the system.
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 of describing the most peculiar features of cuprates held responsible for their anomalous behavior. COM is designed to endorse, since its foundation, the systematic emergence in any SCS of new elementary excitations described by composite operators obeying noncanonical 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 noncrossing 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 versus small Fermi surface dichotomy, Fermi surface deconstruction (appearance of Fermi arcs), nodal versus antinodal physics, pseudogap(s), and 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 antinodal dynamics in the underdoped regime.
The two-dimensional Hubbard model is studied within the composite operator method (COM) with the self-energy computed in the self-consistent Born approximation (SCBA). The COM describes interacting electrons in terms of the new elementary excitations that appear in the system owing to strong correlations; residual interactions among these excitations are treated within the SCBA. On decreasing the doping (from the overdoped to underdoped region), anomalous features develop in the spectral function $A(\mathbf{k},\ensuremath{\omega})$, the Fermi surface, the momentum distribution function n(k), the dispersion, and the density of states $N(\ensuremath{\omega})$ in the intermediate-coupling regime (U=8) at low temperatures (T=0.01−−0.02). At high doping (n=0.7), the system resembles an ordinary weakly interacting metal. At low doping (n=0.92), a pseudogap opens, hot and cold spots appear, and non-Fermi-liquid features develop. This behavior, together with the presence of kinks in the calculated electronic dispersion, is in agreement with angle-resolved photoemission spectroscopy data for high-Tc cuprates superconductors.
In this work we investigate some aspects of the physics of strongly correlated systems by taking into account both electron-electron and electron-phonon interactions as basic mechanisms for reproducing electronic correlations in real materials. The relevance of the electron-electron interactions is discussed in the first part of this thesis in the framework of a self-consistent theoretical approach, named Composite Operator Method (COM), which accounts for the relevant quasi-particle excitations in terms of a set of composite operators that appear as a result of the modification imposed by the interactions on the canonical electronic fields. We show that the COM allows the calculation of all the relevant Green’s and correlation functions in terms of a number of unknown internal parameters to be determined self-consistently. Therefore, depending on the balance between unknown parameters and self-consistent equations, exact and approximate solutions can be obtained. By way of example, we discuss the application of the COM to the extended t-U- J-h model in the atomic limit, and to the two-dimensional single-band Hubbard model. In the former case, we show that the COM provides the exact solution of the model in one dimension. We study the effects of electronic correlations as responsible for the formation of a plethora of different charge and/or spin orderings. We report the phase diagram of the model, as well as a detailed analysis of both zero and finite temperature single-particle and thermodynamic properties. As far as the single-band Hubbard model is concerned, we illustrate an approximated selfconsistent scheme based on the choice of a two-field basis. We report a detailed analysis of many unconventional features that arise in single-particle properties, thermodynamics and system’s response functions. We emphasize that the accuracy of the COM in describing the effects of electronic correlations strongly relies on the choice of the basis, paving the way for possible multi-pole extensions to the twofield theory. To this purpose, we also study a three-field approach to the single-band Hubbard model, showing a significant step forward in the agreements with numerical data with respect to the two-pole results. The role of the electron-phonon interaction in the physics of strongly correlated systems is discussed in the second part of this thesis. We show that in highly polarizable lattices the competition between unscreened Coulomb and Fröhlich interactions results in a short-range polaronic exchange term Jp that favours the formation of local and light pairs of bosonic nature, named bipolarons, which condense with a critical temperature well in excess of hundred kelvins. These findings, discussed in the framework of the so-called polaronic t-Jp model, are further investigated in the presence of a finite on-site potential ~U , coming from the competition between on-site Coulomb and Fröhlich interactions. We discuss the role of ~U as the driving parameter for a small-to-large bipolaron transition, providing a possible explanation of the BEC-BCS crossover in terms of the properties of the bipolaronic ground state. Finally, we show that a hard-core bipolarons gas, studied as a charged Bose-Fermi mixture, allows for the description of many non Fermi liquid behaviours, allowing also for a microscopic explanation of pseudogap features in terms of a thermal-induced recombination of polarons and bipolarons, without any assumption on preexisting order or broken symmetries. [edited by Author]