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Acta Physica Polonica A

t-J Model Then and Now: a Personal Perspective from the Pioneering Times

Józef Spałek

Published Apr 1, 2007• 70 citations
Publisher

Abstract

In this overview we sketch briefly the path to the so-called 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 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 they were transformed into mathematical language.The concept of hybrid pairing is introduced in the same context at the end.

DOI
10.12693/aphyspola.111.409

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In this overview we sketch briefly the path to the so-called 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 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 they were transformed into mathematical language.The concept of hybrid pairing is introduced in the same context at the end.
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 they were transformed into mathematical language. The concept of {\em hybrid pairing} is introduced in the same context at the end.
I briefly overview the original formulation of the t-J model starting from Hubbard model, as well as stress its unique features, i.e., advantages and shortcomings when discussing its physical properties. Particular emphasis is put on a brief characterization of connection between magnetism, unconventional superconductivity, and the Mott-Hubbard localization of the correlated carriers in a narrow band. In the second part I summarize the model generalization to the three--orbital situation. The main purpose is to list some basic features of the physics associated with t--J model.
In this brief overview, I address some of the fundamental topics related to the physics of strongly correlated fermions, which have been also the subject of my research. After addressing the question why the field has a fundamental meaning, we next turn to the specific problems with their simple theoretical description. Those topics are: (i) the concept of spindependent masses of heavy particles and its subsequent experimental verification; (ii) the correlated metal–insulator transitions of the Mott–Hubbardtype; (iii) real space pairing and its subsequent experimental verification for high-temperature superconducting cuprates. I mention also the persistence of quantum spin and charge excitations in the superconducting phase. All those phenomena confirm the view that the strongly correlated fermionic \nsystems represent a new class of quantum liquids, with some properties quantitatively different than those of the Landau Fermi liquids. Namely, they can be classified as those that fall in between those of the anomalous Landau Fermi liquid and localized-magnetic-moment system.
In these lecture notes, recent theoretical and experimental work on quantum phase transitions, in particular, in metals with strong electronic interactions will be reviewed. After an introduction to classical and quantum phase transitions, we will briefly discuss the standard model of metals, i.e., the Landau Fermi‐liquid theory, and routes to non‐Fermi‐liquid behavior. We will then focus on two different types of quantum phase transitions, magnetic quantum phase transitions in heavy‐fermion systems, and metal‐insulator transitions in heavily doped semiconductors.
We use the concept of generalized (almost localized) Fermi Liquid composed of nonstandard quasiparticles with spin-dependence effective masses and the effective field induced by electron correlations.This Fermi liquid is obtained within the so-called statistically-consistent Gutzwiller approximation (SGA) proposed recently [cf.J. Je ¸drak et al., arXiv: 1008.0021] and describes electronic states of the correlated quantum liquid.Particular emphasis is put on real space pairing driven by the electronic correlations, the Fulde-Ferrell state of the heavy-fermion liquid, and the d-wave superconducting state of high temperature cuprate superconductors in the overdoped limit.The appropriate phase diagrams are discussed showing in particular the limits of stability of the Bardeen-Cooper-Schrieffer (BCS) type of state.