Mobile impurity in one-dimensional correlated electron systems

1998 ◽  
Vol 5 (3) ◽  
pp. 479-486 ◽  
Author(s):  
Y. Tsukamoto ◽  
T. Fujii ◽  
N. Kawakami
Keyword(s):  
Electron Systems ◽  
Correlated Electron Systems ◽  
One Dimensional ◽  
Correlated Electron

Exact Results for Highly Correlated Electron Systems in One Dimension

1997 ◽  
Vol 11 (04n05) ◽  
pp. 355-667 ◽  
Author(s):  
P. Schlottmann
Keyword(s):  
Hubbard Model ◽  
One Dimension ◽  
Correlated Electrons ◽  
Exact Results ◽  
Electron Systems ◽  
Persistent Currents ◽  
Correlated Electron Systems ◽  
One Dimensional ◽  
Correlated Electron ◽  
Highly Correlated

One-dimensional conductors are a long-standing topic of research with direct applications to organic conductors and mesoscopic rings. The discovery of the ceramic high-temperature superconductors has revitalized the interest in low-dimensional charge and spin fluctuations of highly correlated electron systems. Several mechanisms proposed to explain the high-T c superconductors invoke properties of the two-dimensional Hubbard model, but probably also some one-dimensional aspects are relevant. Numerous one-dimensional models for correlated electrons have been studied with various approximate, asymptotically exact and exact methods. These results lead to the concept of Luttinger liquid for interacting electron gases without excitation gaps (metallic systems). Characteristic of Luttinger liquids are the charge and spin separation, marginal Fermi liquid properties, e.g. the absence of quasiparticles in the vicinity of the Fermi surface, nonuniversal power-law singularities in the one-particle spectral function and the related absence of a discontinuity in the momentum distribution at the Fermi level, the power-law decay of correlation functions for long times and large distances, persistent currents in finite rings, etc. Due to the peculiarities of the phase space in one dimension some of the models have sufficient conserved currents to be completely integrable. We review exact results derived within the framework of Bethe's ansatz for integrable one-dimensional models of correlated electrons. The Bethe-ansatz method is presented by explicitly showing the steps leading to the solution of the N-component electron gas interacting via a δ-function potential (repulsive and attractive interaction), which is probably the simplest model of correlated electrons. Emphasis is given to the procedure to extract the groundstate properties, the classification of states, the excitation spectrum, the thermodynamics and finite size effects, such as critical exponents of correlation functions and persistent currents. The method is then applied to numerous other models, e.g. (i) a two-band model involving attractive and repulsive potentials and crystalline fields splitting the bands, (ii) the traditional Hubbard chain with attractive and repulsive U, (iii) the degenerate Hubbard model with repulsive U, which displays a metal–insulator transition at a finite U, (iv) a two-band Hubbard model with repulsive U, (v) the traditional supersymmetric t–J model (vi) a two-band supersymmetric t–J model with band-splitting and (vii) the N-component supersymmetric t–J model. Finally, results for models with long-range interactions, in particular r-2 and sinh -2(r) potentials, are briefly reviewed.

EIGEN-FUNCTIONAL METHOD AND EIKONAL-TYPE EQUATIONS IN ONE-DIMENSIONAL STRONGLY CORRELATED ELECTRON SYSTEMS

2002 ◽  
Vol 16 (16) ◽  
pp. 2201-2220 ◽  
Author(s):  
YU-LIANG LIU
Keyword(s):  
Functional Method ◽  
Electron Interaction ◽  
Large Momentum ◽  
Strongly Correlated Electron Systems ◽  
Strongly Correlated ◽  
Electron Systems ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
One Dimensional ◽  
Correlated Electron

Using eigen-functional method, we study one-dimensional strongly correlated electron systems with large momentum (2k F and/or 4k F ) transfer term(s), and demonstrate that this kind of problems ends in to solve the Eikonal-type equations, and these equations are universal, and independent of whether or not the system is integrable. In contrast to usual perturbation theory, this method is valid not only for weak electron interaction, but also for strong electron interaction. Comparing with exact solution of some integrable models, it can give correct results in linearization approximation. This method can also be used to study electron-phonon interaction systems, and two coupled spin chain (or quantum wire) systems.

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