The Hubbard model within the equations of motion approach

Abstract

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.

232 pages, more than 300 figures, more than 500 references

References in corpus (7)

• Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
• Bosonic sector of the two-dimensional Hubbard model studied within a two-pole approximation
• The Hubbard model with intersite interaction within the Composite Operator Method
• The energy-scale-dependent Composite Operator Method for the single-impurity Anderson model
• Non-Ergodicity of the 1D Heisenberg Model
• Effects of two-site composite excitations in the Hubbard model
• Antiferromagnetism in the 2D Hubbard model: phase transition and local quantities

Cited by in corpus (27)

• Fate of the false Mott-Hubbard transition in two dimensions
• One-dimensional extended Hubbard model in the atomic limit
• Field-driven attosecond photoinjection dynamics in semiconductors
• Underdoped cuprates phenomenology in the 2D Hubbard model within COM(SCBA)
• Composite Operator Method analysis of the underdoped cuprates puzzle
• Fermionic systems with charge correlations
• Exact solution of the one-dimensional spin-$\frac{3}{2}$ Ising model in magnetic field
• Extended Hubbard model in the presence of a magnetic field
• The Hubbard model with intersite interaction within the Composite Operator Method
• Quasiparticle states of the Hubbard model near the Fermi level
• Magnetic susceptibility of the two-dimensional Hubbard model using a power series for the hopping constant
• Equations of motion approach to the spin-1/2 Ising model on the Bethe lattice
• New perspectives on the Ising model
• Bands renormalization and superconductivity in the strongly correlated Hubbard model using composite operators method
• Composite Orders and Lifshitz Transition of Heavy Electrons
• Unconventional orbital ordering and emergent dimensional reduction in fulleride superconductors
• TR-ARPES Signal in Pumped Semiconductors within Dynamical Projective Operatorial Approach (DPOA)
• Study of the spin-$\frac{3}{2}$ Hubbard-Kondo lattice model by means of the Composite Operator Method
• Quasi-particle propagation across semiconductor-Mott insulator interfaces
• Electronic spectrum and superconductivity in the extended t-J-V model
• Role of the attractive intersite interaction in the extended Hubbard model
• Bound States at Semiconductor -- Mott Insulator Interfaces
• Local properties of the t-J model in a two-pole approximation within COM
• Superconductivity and superconducting order parameter phase fluctuations in a weakly doped antiferromagnet
• Transmission through multiple Mott insulator - semiconductor wells
• Fermionic systems with charge correlations on the Bethe lattice
• COM(3p) solution of the 2D Hubbard model: momentum resolved quantities