The Hubbard model within the equations of motion approach (original) (raw)
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Emery vs. Hubbard model for cuprate superconductors: a composite operator method study
The European Physical Journal B, 2013
Within the Composite Operator Method (COM), we report the solution of the Emery model (also known as p-d or three band model), which is relevant for the cuprate high-Tc superconductors. We also discuss the relevance of the often-neglected direct oxygen-oxygen hopping for a more accurate, sometimes unique, description of this class of materials. The benchmark of the solution is performed by comparing our results with the available quantum Monte Carlo ones. Both singleparticle and thermodynamic properties of the model are studied in detail. Our solution features a metal-insulator transition at half filling. The resulting metal-insulator phase diagram agrees qualitatively very well with the one obtained within Dynamical Mean-Field Theory. We discuss the type of transition (Mott-Hubbard (MH) or charge-transfer (CT)) for the microscopic (ab-initio) parameter range relevant for cuprates getting, as expected a CT type. The emerging single-particle scenario clearly suggests a very close relation between the relevant sub-bands of the three-(Emery) and the single-band (Hubbard) models, thus providing an independent and non-perturbative proof of the validity of the mapping between the two models for the model parameters optimal to describe cuprates. Such a result confirms the emergence of the Zhang-Rice scenario, which has been recently questioned. We also report the behavior of the specific heat and of the entropy as functions of the temperature on varying the model parameters as these quantities, more than any other, depend on and, consequently, reveal the most relevant energy scales of the system. arXiv:1306.3263v1 [cond-mat.str-el]
The Hubbard model with intersite interaction within the Composite Operator Method
The European Physical Journal B Condensed Matter Physics, 2004
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.
ARPES-parameterized Hubbard approach to d-wave cuprate superconductors
2014
In the last decade, the Angle Resolved Photoemission Spectroscopy (ARPES) has achieved important advances in both energy and angular resolutions, providing a direct measurement of the single-particle dispersion relation and superconducting gap. These dispersion relation data allow a full determination of the self-energy, first and second neighbor parameters in the Hubbard model. This model and its generalizations offer a simple and general way to describe the electronic correlation in solids. In particular, the parameters of correlated hopping interactions, responsible of the dwave superconductivity in the generalized Hubbard model, are determined from ARPES data and the critical temperature within the mean-field approximation. In this work, we determine the model parameters for Bi 2 Sr 2-x La x CuO 6+δ and study its d-wave superconducting gap as a function of temperature by solving numerically two coupled integral equations. Finally, the calculated electronic specific heat is compared with experimental results.
Numerical studies of the Hubbard model
Nuclear Physics B - Proceedings Supplements, 1991
Numerical studies of the two-dimensional Hubbard model have shown that it exhibits the basic phenomena seen in the cuprate materials. At half-filling one finds an antiferromagnetic Mott-Hubbard groundstate. When it is doped, a pseudogap appears and at low temperature d-wave pairing and striped states are seen. In addition, there is a delicate balance between these various phases. Here we review evidence for this and then discuss what numerical studies tell us about the structure of the interaction which is responsible for pairing in this model. stripes, pseudogap behavior, and d x 2 −y 2 pairing. In addition, the numerical studies have shown how delicately balanced these models are between nearly degenerate phases. Doping away from half-filling can tip the balance from antiferromagnetism to a striped state in which half-filled domain walls separate π-phase-shifted antiferromagnetic regions. Altering the next-near-neighbor hopping t ′ or the strength of U can favor d x 2 −y 2 pairing correlations over stripes. This delicate balance is also seen in the different results obtained using different numerical techniques for the same model. For example, density matrix renormalization group (DMRG) calculations for doped 8-leg t-J ladders find evidence for a striped ground state. [12] However, variational and Green's function Monte Carlo calculations for the doped t-J lattice, pioneered by Sorella and co-workers, [23, 24] find groundstates characterized by d x 2 −y 2 superconducting order with only weak signs of stripes. Similarly, DMRG calculations for doped 6-leg Hubbard ladders [14] find stripes when the ratio of U to the near-neighbor hopping t is greater than 3, while various cluster calculations [27, 30-33] find evidence that antiferromagnetism and d x 2 −y 2 superconductivity compete in this same parameter regime. These techniques represent present day state-of-the-art numerical approaches. The fact that they can give different results may reflect the influence of different boundary conditions or different aspect ratios of the lattices that were studied. The n-leg open boundary conditions in the DMRG calculations can favor stripe formation. Alternately, the cluster lattice sizes and boundary conditions can frustrate stripe formation. It is also possible that these differences reflect subtle numerical biases in the different numerical methods. Nevertheless, these results taken together show that both the striped and the d x 2 −y 2 superconducting phases are nearly degenerate low energy states of the doped system. Determinantal quantum Monte Carlo calculations [21] as well as various cluster calculations show that the underdoped Hubbard model also exhibits pseudogap phenomena. [27-32] The remarkable similarity of this behavior to the range of phenomena observed in the cuprates provides strong evidence that the Hubbard and t-J models indeed contain a significant amount of the essential physics of the problem. [34]
The 1D Hubbard model within the Composite Operator Method
The European Physical Journal B, 2002
Although effective for two dimensional (2D) systems, some approximations may fail in describing the properties of one-dimensional (1D) models, which belong to a different universality class. In this paper, we analyze the adequacy of the Composite Operator Method (COM ), which provides a good description of many features of 2D strongly correlated systems, in grasping the physics of 1D models. To this purpose, the 1D Hubbard model is studied within the framework of the COM by considering a two-pole approximation and a paramagnetic ground state. The local, thermodynamic and single-particle properties, the correlation functions and susceptibilities are calculated in the case of half filling and arbitrary filling. The results are compared with those obtained by the Bethe Ansatz (BA) as well as by other numerical and analytical techniques. The advantages and limitations of the method are analyzed in detail.
Physica B: Condensed Matter, 2005
The Roth's two-pole approximation has been used by the present authors to study the effects of the hybridization in the superconducting properties of a strongly correlated electron system. The model used is the extended Hubbard model which includes the d − p hybridization, the p-band and a narrow d-band. The present work is an extension of the previous Ref. [3]. Nevertheless, some important correlation functions necessary to estimate the Roth's band shift, are included together with the temperature T and the Coulomb interaction U to describe the superconductivity. The superconducting order parameter of a cuprate system, is obtained following Beenen and Edwards formalism. Here, we investigate in detail the change of the order parameter associated to temperature, Coulomb interaction and Roth's band shift effects on superconductivity. The phase diagram with Tc versus the total occupation numbers nT , shows the difference respect to the previous work.
Journal of Physics and Chemistry of Solids, 2011
The two-dimensional Hubbard model in the superconducting d-wave phase has been solved within the Composite Operator Method (COM) in the two-pole approximation . The unknowns of the theory have been computed exploiting the operatorial relations, dictated by the Pauli principle, existing between the composite operators belonging to the basis. Such a procedure has also allowed to correctly fix the Hilbert space of the problem avoiding to average on unphysical states and permitting to obtain a very good qualitative agreement with the experimental results available in the literature as regards the phase diagram in the T-n plane. Given such an encouraging result, in this short manuscript, we have analyzed the filling and temperature dependence of the static and uniform spin susceptibility, as obtained by means of the COM within a one-loop-like approximation, and we have compared them to the experimentally observed ones for single-layer high-Tc cuprate superconductors.
Superconductivity in an extended Hubbard model with attractive interaction
Superconductor Science and Technology, 2011
In this work, a two-dimensional one-band Hubbard model is investigated within a two-pole approximation. The model presents a non-local attractive potential U (U < 0) that allows the study of d-wave superconductivity and also includes hopping up to second-nearest-neighbors. The twopole scheme has been proposed to improve the Hubbard-I approximation. The analytical results
A 4-pole approach to the Hubbard model within the Composite Operator Method
Journal of Physics: Conference Series, 2012
The Hubbard model is studied within the Composite Operator Method framework in a 4-pole approximation. The operatorial basis is chosen according to both the hierarchy of equations of motion and the exact solution of the model reduced to the minimal cluster (2 sites) where all Hamiltonian terms are still active. Such a recipe amounts to include into the basis not only the two Hubbard operators, which usually take care of the scale of energy related to the on-site Coulomb repulsion U , but also two other non-local operators describing the Hubbard operators dressed by charge, spin and pair fluctuations on the nearest-neighboring sites and addressing the dynamically generated scale of energy related to the exchange J = 4t 2 /U . The calculation framework is outlined and a very first comparison to numerical simulations, showing very good qualitative and quantitative agreement, is reported. As reference, the results in the 2-pole approximation are also reported and the differences discussed.