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Journal of Physical Studies

Single-particle properties of the extended Hubbard model in the composite operator method

Adolfo Avella, Francesco Paolo Mancini, M. M. Sánchez

Published Jan 1, 1998• 3 citations
Publisher

Abstract

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.

DOI
10.30970/jps.02.232

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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.
We present a novel solution of the 2D Hubbard model in the framework of the Composite Operator Method within a four-pole approximation. We adopt a basis of four fields: the two Hubbard operators plus two fields describing the Hubbard transitions dressed by nearest-neighbor spin fluctuations. We include these nonlocal operators because spin fluctuations play a dominant role in strongly correlated electronic systems with respect to other types of nonlocal charge, pair and double-occupancy fluctuations. The approximate solution performs very well once compared with advanced (semi-) numerical methods from the weak-to the strong-coupling regime, being by far less computational-resource demanding. We adopt this solution to study the single-particle properties of the model in the strong coupling regime, where the effects of strong short-range magnetic correlations are more relevant and could be responsible for anomalous features. In particular, we will focus on the characterization of the Fermi surface and of its evolution with doping.
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)n(\mathbf{k})n(k), the dispersion, and the density of states $N(\ensuremath{\omega})$ in the intermediate-coupling regime (U=8)(U=8)(U=8) at low temperatures (T=0.01−−0.02)(T=0.01--0.02)(T=0.01−−0.02). At high doping (n=0.7)(n=0.7)(n=0.7), the system resembles an ordinary weakly interacting metal. At low doping (n=0.92)(n=0.92)(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{T}_{c}Tc​ cuprates superconductors.
Anomalous properties of the normal state of a strongly correlated electron system described by an attractive extended Hubbard model are investigated. The equations of motion of the Green’s functions are calculated with the two-pole approximation which gives rise to quasiparticle renormalized bands. The two-pole approximation leads to a set of correlation functions. In particular, the antiferromagnetic correlation function plays an important role as a source of anomalies in the normal state of the model. The uniform static magnetic susceptibility as a function of occupation n T and temperature is calculated. At low temperatures, the susceptibility presents a peak for n T ≃ 0.80. The results suggest that it is the onset of short-range antiferromagnetic correlations, which could be a mechanism for the pseudogap. The Fermi surface, defined by the spectral function , is presented for different dopings. It has been observed that above n T ≃ 0.80 the ordinary Fermi surface evolves to a hole pocket with pseudogaps near the antinodal points (0,π) and (π,0).
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.
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 $p\ensuremath{-}d$ model which well describes the CuO2{\mathrm{CuO}}_{2}CuO2​ planes of the high-Tc{T}_{c}Tc​ superconductors is studied by means of the composite operator method. The relevant quasiparticle excitations are represented by composite operators. As a result of taking into account spin excitations we find a p-like band near the Fermi level. The dispersion of this band gives a Fermi surface which is in good agreement with the experimental measurements. Due to the strong mixing of the relevant excitations, the spectral weight of this band is reduced and gives a large Fermi surface in the moderately doped region. The dependence of the calculated physical quantities on model parameters, temperature and doping, is in very good agreement with the available quantum Monte Carlo results.