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 (115)

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• Tricritical Behavior in the Extended Hubbard Chains
• Incommensurate Magnetic Fluctuations in YBa2Cu3O6.6
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• Superconductivity mediated by charge fluctuations in layered molecular crystals
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• Electronic Structure of La2-xSrxCuO4 in the Vicinity of the Superconductor-Insulator Transition
• Competing orders and quantum criticality in doped antiferromagnets
• Doping Dependent Density of States and Pseudogap Behavior in La2-xSrxCuO4
• Ground-state phase diagram of a half-filled one-dimensional extended Hubbard model
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• Theory of electron-hole asymmetry in doped {\em CuO${}_2$} planes
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• Phase Diagram of the Extended Hubbard Model with Correlated Hopping Interaction
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• The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties
• Charge ordering and antiferromagnetic exchange in layered molecular crystals of the theta type
• Theory of spin and charge fluctuations in the Hubbard model
• ARPES Spectra of the Hubbard model
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• Exact ground states of generalized Hubbard models
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• Dynamical Mean Field Theory of the Antiferromagnetic Metal to Antiferromagnetic Insulator Transition
• Influence of next-nearest-neighbor electron hopping on the static and dynamical properties of the 2D Hubbard model
• Spin-wave excitation spectra and spectral weights in square lattice antiferromagnets
• Thermodynamic properties of the planar $t-J$ model
• Quantum Electron Liquids and High-Tc Superconductivity
• Specific Heat of the 2D Hubbard Model
• Violation of Luttinger's Theorem in the Two-Dimensional t-J Model
• Thermodynamics of the planar Hubbard model
• Theory for Electron-Doped Cuprate Superconductors: d-wave symmetry order parameter
• Spin wave dispersion in La2CuO4
• Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
• The moment sum rule and its consequences for ferromagnetism in the Hubbard model
• Metal-insulator transition and charge ordering in the extended Hubbard model at one-quarter filling
• The Hubbard model in the two-pole approximation
• Mott Transitions in the 2D Half-Filled Hubbard Model: Correlator Projection Method with Projective Dynamical Mean-Field Approximation
• Energy level statistics of the two-dimensional Hubbard model at low filling
• Optical properties of an effective one-band Hubbard model for the cuprates
• Excitons in C_60 studied by Temperature Dependent Optical Second- Harmonic Generation
• Is there spin-charge separation in the 2D Hubbard and t-J models at low electronic densities?
• Pseudogap in Doped Mott Insulators is the Near-neighbour Analogue of the Mott Gap
• Hole Doping Evolution of the Quasiparticle Band in Models of Strongly Correlated Electrons for the High-T_c Cuprates
• Superconducting, ferromagnetic and antiferromagnetic phases in the t-t' Hubbard model
• Indications of a Metallic Antiferromagnetic Phase in the 2 Dimensional $U-t-t^{\prime }$ Model
• Charge and Spin Gap Formation in Exactly Solvable Hubbard Chains with Long-Rang Hopping
• Increasing d-wave superconductivity by on site repulsion
• Filling-Control Metal-Insulator Transition in the Hubbard Model Studied by the Operator Projection Method
• Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects
• Equation of Motion Method for Composite Field Operators
• Strong coupling theory for the Hubbard model
• d_{x^2-y^2} pairing of composite excitations in the 2D Hubbard model
• Bosonic sector of the two-dimensional Hubbard model studied within a two-pole approximation
• A Study of the Antiferromagnetic Phase in the Hubbard Model by means of the Composite Operator Method
• Phase Diagram of the Half-Filled Extended Hubbard Model in Two Dimensions
• The 2-site Hubbard and t-J models
• The Mott-Hubbard transition and the paramagnetic insulating state in the two-dimensional Hubbard model
• Operator projection method applied to the single-particle Green's function in the Hubbard model
• The two-dimensional t-t'-U model as a minimal model for cuprate materials
• Incommensurate magnetism in cuprate materials
• Theory of the Reentrant Charge-Order Transition in the Manganites
• Local Dynamics and Strong Correlation Physics I: 1D and 2D Half-filled Hubbard Models
• Two-scale analysis of the SU(N) Kondo Model
• The Hubbard model with intersite interaction within the Composite Operator Method
• The overdoped regime in LSCO
• Charged excitons in doped extended Hubbard model systems
• Conservation of the spectral moments in the n-pole approximation
• Incommensurate spin fluctuations in the two-dimensional t-t'-U model
• Spin wave dispersion softening in the ferromagnetic Kondo lattice model for manganites
• The 1D Hubbard model within the Composite Operator Method
• The energy-scale-dependent Composite Operator Method for the single-impurity Anderson model
• Pseudospin SU(2) Symmetry Breaking, Charge Density Wave and Superconductivity in the Hubbard Model
• Local properties and Density of States in the two-dimensional p-d Model
• The half-filled Hubbard chain in the Composite Operator Method: A comparison with Bethe Ansatz
• Weak Coupling Phases of the Attractive $t-t^{\prime }$ Hubbard Model at the Van Hove Filling
• Non-Ergodicity of the 1D Heisenberg Model
• s-s*-d-wave superconductor on a square lattice and its BCs phase diagram
• Spin susceptibility and magnetic short-range order in the Hubbard model
• Electronic specific heat in the normal state of cuprate high-Tc superconductors
• Hole Pockets in the Doped 2D Hubbard Model
• Effects of two-site composite excitations in the Hubbard model
• Symmetry Properties on Magnetization in the Hubbard Model at Finite Temperatures
• Local properties in the two-dimensional t-t'-U model
• The Conductivity Tensor for the Hubbard Model
• Magnetic properties of the 2D t-t'-Hubbard model
• Antiferromagnetism in the 2D Hubbard model: phase transition and local quantities
• Exact properties of the chemical potential-density relation at finite temperature in the Hubbard model
• New Comparisons for Local Quantities of the Two-Dimensional Hubbard Model
• The N-Chain Hubbard model in the Composite Operator Method
• Spin magnetic susceptibility in the two-layer Hubbard model

Cited by in corpus (56)

• Fate of the false Mott-Hubbard transition in two dimensions
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Optical and DC conductivity of the two-dimensional Hubbard model in the pseudogap regime and across the antiferromagnetic quantum critical point, including vertex corrections
• Electronic spectrum in high-temperature cuprate superconductors
• 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)
• Emery vs. Hubbard model for cuprate superconductors: a Composite Operator Method study
• The extended Hubbard model in the ionic limit
• High-order correlation effects in the two-dimensional Hubbard model
• Composite Operator Method analysis of the underdoped cuprates puzzle
• The Hubbard model beyond the two-pole approximation: a Composite Operator Method study
• The Composite Operator Method (COM)
• 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
• Polaron transformations in the realistic model of the strongly correlated electron system
• Fermionic systems with charge correlations
• The Hubbard model with intersite interaction within the Composite Operator Method
• Projective Truncation Approximation for Equations of Motion of Two-Time Green's Functions
• Charge dynamics of correlated electrons: Variational description with inclusion of composite fermions
• Non-ergodic dynamics of the extended anisotropic Heisenberg chain
• Equations of motion approach to the spin-1/2 Ising model on the Bethe lattice
• Magnetic susceptibility of the two-dimensional Hubbard model using a power series for the hopping constant
• Quasiparticle states of the Hubbard model near the Fermi level
• Spectral properties of four-time fermionic Green's functions
• New perspectives on the Ising model
• Itinerant and local-moment magnetism in strongly correlated electron systems
• Exact solution of the 1D Hubbard model in the atomic limit with inter-site magnetic coupling
• Two-step dynamics of photoinduced phonon entanglement generation between remote electron-phonon systems
• Bands renormalization and superconductivity in the strongly correlated Hubbard model using composite operators method
• Composite Orders and Lifshitz Transition of Heavy Electrons
• Two-Particle-Self-Consistent Approach for the Hubbard Model
• Singularity in self-energy and composite fermion excitations of interacting electrons
• The two-orbital Hubbard model and the OSMT
• Magnon and Hole Excitations in the Two-Dimensional Half-filled Hubbard Model
• Unconventional orbital ordering and emergent dimensional reduction in fulleride superconductors
• Controllable Precision of the Projective Truncation Approximation for Green's Functions
• Spin and charge orderings in the atomic limit of the U-V-J model
• Different orderings in the narrow-band limit of the extended Hubbard model on the Bethe lattice
• TR-ARPES Signal in Pumped Semiconductors within Dynamical Projective Operatorial Approach (DPOA)
• The composite operator method route to the 2D Hubbard model and the cuprates
• Study of the spin-$\frac{3}{2}$ Hubbard-Kondo lattice model by means of the Composite Operator Method
• Effect of Coulomb repulsion on the London penetration depth in cuprate superconductors
• Quasi-particle propagation across semiconductor-Mott insulator interfaces
• Entanglement Properties and Phase Diagram of the Two-Orbital Atomic Hubbard Model
• Single-particle properties of the Hubbard model in a novel three-pole approximation
• Role of the attractive intersite interaction in the extended Hubbard model
• Electronic spectrum and superconductivity in the extended t-J-V model
• Equation of motion truncation scheme based on partial orthogonalization
• Superconductivity and superconducting order parameter phase fluctuations in a weakly doped antiferromagnet
• Bound States at Semiconductor -- Mott Insulator Interfaces
• Local properties of the t-J model in a two-pole approximation within COM
• Transmission through multiple Mott insulator - semiconductor wells
• On non-canonical degrees of freedom
• COM(3p) solution of the 2D Hubbard model: momentum resolved quantities
• Fermionic systems with charge correlations on the Bethe lattice