# t-J model then and now: A personal perspective from the pioneering times

@article{Spalek2007tJMT,
title={t-J model then and now: A personal perspective from the pioneering times},
author={J{\'o}zef Spalek},
journal={arXiv: Strongly Correlated Electrons},
year={2007}
}
• J. Spalek
• Published 1 April 2007
• Physics
• arXiv: Strongly Correlated Electrons
In this overview I sketch briefly the path to the so-called {\em t-J model} derived for the first time 30 years ago and provide its original meaning within the theory of strongly correlated magnetic metals with a non-Fermi (non-Landau) liquid ground state. An emergence of the concept of {\em real space pairing}, is discussed in a historical prospective. A generalization of this model to the many-orbital situation is briefly discussed. The emphasis is put on didactical exposition of ideas, as…
62 Citations
Fifty years of Hubbard and Anderson lattice models: from magnetism to unconventional superconductivity - A brief overview
We briefly overview the importance of the Hubbard- and Anderson-lattice models as applied to the explanation of high-temperature and heavy-fermion superconductivity. Application of the models during
A generalized mean-field theory for the t-J model: the single-pole COM solution
• Physics
The European Physical Journal Special Topics
• 2019
We have reported the most general mean-field approximation for the t-J model obtained in the framework of the Composite Operator Method within the simplest one-pole approximation. The
Anderson lattice with explicit Kondo coupling revisited: metamagnetism and the field-induced suppression of the heavy fermion state.
• Physics
Journal of physics. Condensed matter : an Institute of Physics journal
• 2012
The extended (statistically consistent, SCA) Gutzwiller-type approach to the periodic Anderson model (PAM) in an applied magnetic field and in the strong-correlation limit shows that in ferromagnetic phases the low-energy single-particle states are strongly affected by the presence of the applied magnetic fields.
Slave particle study of the strongly correlated electrons
Until three decades ago, our understanding of the condensed matter systems were based on two frameworks developed by Russian physicist Lev Landau: his theory of phase transition, and Fermi liquids.
Exchange interaction as the source of pairing in correlated electron systems: a brief overview
We address the question of real space pairing induced by exchange interaction, customarily associated with the presence of the broken-symmetry magnetism. For such mechanism of pairing, the appearance
Surprises in the t-J Model: Implications for Cuprates.
• Physics
Physical review letters
• 2020
An analysis of the t-J model in the slave boson formulation which accounts for strong correlations, focusing on fluctuation effects that have hitherto not received the attention they deserve, finds several interesting results including the instability of the d-wave superconducting state to internal phase fluctuations giving way to a time reversal broken d+is^{*} superconductor at low doping.
Doublon dynamics in the extended Fermi-Hubbard model
• Physics
• 2012
Two fermions occupying the same site of a lattice model with strongly repulsive Hubbard-type interaction U form a doublon, a long-living excitation the decay of which is suppressed because of energy
Antiferromagnetism, charge density wave, and d-wave superconductivity in the extended t-J-U model: role of intersite Coulomb interaction and a critical overview of renormalized mean field theory.
• Physics
Journal of physics. Condensed matter : an Institute of Physics journal
• 2017
The role of the intersite Coulomb interaction term V in stabilizing the CDW phase is concentrated on, and it is shown that the charge ordering appears only above a critical value of V in a limited hole-doping range δ.
A More Complete Model for High-Temperature Superconductors
To date, the Hubbard model and its strong coupling limit, the t - J model, serve as the canonical model for strongly correlated electron systems in solids. Approximating the Coulomb interaction by
A More Complete Model for High-Temperature Superconductors
To date, the Hubbard model and its strong coupling limit, the t-J model, serve as the canonical model for strongly correlated electron systems in solids. Approximating the Coulomb interaction by only

## References

SHOWING 1-10 OF 17 REFERENCES
Relation between the Anderson and Kondo Hamiltonians
• Physics
• 1966
A canonical transformation is used to relate the Anderson model of a localized magnetic moment in a dilute alloy to that of Kondo. In the limit of small $s\ensuremath{-}d$ mixing, which is the most
Electron correlations in narrow energy bands
• J. Hubbard
• Physics
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
• 1963
It is pointed out that one of the main effects of correlation phenomena in d- and f-bands is to give rise to behaviour characteristic of the atomic or Heitler-London model. To investigate this
Discontinuous metal-insulator transitions of correlated electrons at nonzero temperature: Effect of the shape of the density of states
• Physics
• 1991
We discuss the effect of the shape of the density of states (DOS) on the discontinuous metal-insulator transitions of the Mott-Hubbard type at nonzero temperature, within an approach proposed by us
The kinetic exchange interaction in doubly degenerate narrow bands
• Physics
• 1977
A canonical transformation is applied to the doubly-degenerate-band Hubbard model with arbitrary n in the strong correlation regime. Projection operators are constructed to project out the splitted
Electron correlations in narrow energy bands III. An improved solution
• J. Hubbard
• Physics
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
• 1964
A more accurate solution of the model (of an 8-band of interacting electrons) discussed in paper I is obtained. The new solution predicts a finite lifetime for the pseudo-particles and also the
A renormalised Hamiltonian approach to a resonant valence bond wavefunction
• Physics
• 1988
The effective Hamiltonian of strongly correlated electrons on a square lattice is replaced by a renormalised Hamiltonian and the factors that renormalise the kinetic energy of holes and the
Localized Magnetic States in Metals
The conditions necessary in metals for the presence or absence of localized moments on solute ions containing inner shell electrons are analyzed. A self-consistent Hartree-Fock treatment shows that
Kinetic exchange interaction in a doubly degenerate narrow band and its application to Fe1-xCoxS2 and Co1-xNixS2
• Physics
• 1980
The authors have derived a rotationally invariant kinetic exchange interaction between strongly correlated electrons in a doubly degenerate narrow band with arbitrary band filling. The results are
Effective Hamiltonian for the superconducting Cu oxides.
• Physics
Physical review. B, Condensed matter
• 1988
Although assuming that doping creates holes primarily on oxygen sites, we derive explicitly a single-band effective Hamiltonian for the high-${T}_{c}$ Cu-oxide superconductors. Cu-O hybridization