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Journal of Physics C Solid State Physics

An integrable one-dimensional Fermi system with magnetic impurities: magnetisation curve at T=0K

Thomas B. Bahder, Edward H. Rezayi, Josef Sak

Published Feb 20, 1984• 4 citations
Publisher

Abstract

A model of a one-dimensional metal containing impurities is studied. The model is diagonalised exactly using the Bethe ansatz assuming that a certain integrability condition is satisfied between the four coupling constants of the electron-electron and electron-impurity interactions. The magnetisation curve is calculated analytically near the onset and at high fields. At intermediate fields it is obtained numerically.

DOI
10.1088/0022-3719/17/5/018

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•Jan 1, 2008•0 citations
A model of a one-dimensional metal containing impurities is studied. The model is diagonalised exactly using the Bethe ansatz assuming that a certain integrability condition is satisfied between the four coupling constants of the electron-electron and electron-impurity interactions. The magnetisation curve is calculated analytically near the onset and at high fields. At intermediate fields it is obtained numerically.
We propose an integrable Kondo problem in a one-dimensional $t\ensuremath{-}J$ model. With the open boundary condition of the wave functions at the impurity sites, the model can be exactly solved via Bethe ansatz for a set of JL,R{J}_{L,R}JL,R​ (Kondo coupling constants) and VL,R{V}_{L,R}VL,R​ (impurity potentials) parametrized by a single parameter ccc. The integrable value of JL,R{J}_{L,R}JL,R​ runs from negative infinity to positive infinity, which allows us to study both the ferromagnetic Kondo problem and the antiferromagnetic Kondo problem in a strongly correlated electron system. Generally, there is a residual entropy for the ground state, which indicates a typical non-Fermi liquid behavior.
The one-dimensional t - J model at the supersymmetric point, J = 2t, with a magnetic impurity of arbitrary spin S is studied exactly using the Bethe ansatz technique. The impurity interacts by spin exchange with the electrons on neighbouring sites of a lattice without destroying the integrability. The discrete Bethe ansatz equations diagonalizing the model, and the thermodynamic equations are derived. The impurity free energy is obtained for arbitrary band filling as a function of temperature and external magnetic field. The impurity can localize up to one itinerant hole, and has in general mixed-valent properties.
A model describing the Anderson impurity in the Bardeen-Cooper-Schriffer superconductor is proven to exhibit hidden integrability and is diagonalized exactly by the Bethe ansatz. Typeset using REVTEX 1 The basic theoretical models describing magnetic impurities in nonmagnetic normal metals, such as the s-d (Kondo) model, the Anderson model, etc., are integrable under two additional conditions [1]: (i) an electron-impurity coupling is assumed to be energy independent, and (ii) a band electron dispersion ε(k) can be linearized around the Fermi level, ε(k) ≃ vF(k − kF), where kF and vF are the Fermi momentum and velocity, respectively. Only under these conditions, both an electron-impurity scattering and an effective electronelectron coupling are described in terms of discontinuous jumps in the Bethe ansatz wave functions. Therefore a linear dispersion of particles and a pointlike particle-impurity coupling are considered now as the necessary mathematical conditions for integrability of the “impurity ” models. Because a carrier dispersion in superconducting metals cannot be linearized,