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Journal of Physics Condensed Matter

Thermodynamics of the n-channel Kondo model for general n and impurity spin S in a magnetic field

Pedro D Sacramento, P. Schlottmann

Published Dec 2, 1991• 25 citations
Publisher

Abstract

The numerical solution of the Bethe ansatz equations of the n-channel Kondo problem is presented. The thermodynamics of the impurity is obtained as a function of temperature, external field, impurity spin S and the number of channels. Three situations have to be distinguished: (i) If n=2S the conduction electrons exactly compensate the impurity spin into a singlet at low temperatures, (ii) if n<2S the impurity spin is only partially compensated (undercompensated), and (iii) if n>2S the impurity spin is said to be overcompensated giving rise to critical behaviour. The results are briefly discussed in the context of magnetic impurities, the quadrupolar Kondo effect, an impurity spin embedded in the Takhtajan-Babujian model and a two-level system interacting with conduction electrons.

DOI
10.1088/0953-8984/3/48/010

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The numerical solution of the Bethe ansatz equations of the n-channel Kondo problem is presented. The thermodynamics of the impurity is obtained as a function of temperature, external field, impurity spin S and the number of channels. Three situations have to be distinguished: (i) If n=2S the conduction electrons exactly compensate the impurity spin into a singlet at low temperatures, (ii) if n<2S the impurity spin is only partially compensated (undercompensated), and (iii) if n>2S the impurity spin is said to be overcompensated giving rise to critical behaviour. The results are briefly discussed in the context of magnetic impurities, the quadrupolar Kondo effect, an impurity spin embedded in the Takhtajan-Babujian model and a two-level system interacting with conduction electrons.
We review analytical and numerical results derived from the Bethe ansatz solution of the n-channel Kondo model of arbitrary spin S as a function of temperature, external field, impurity spin S and the number of channels n. Three situations have to be distinguished: (i) If n = 2S the conduction electrons exactly compensate the impurity spin into a singlet at low temperatures, (ii) if n < 2S the impurity spin is only partially compensated (undercompensated), and (iii) if n > 2S the impurity spin is said to be overcompensated giving rise to critical behaviour. The results are discussed in the context of magnetic impurities, e.g. Fe, Cr and Tm in simple metals, the quadrupolar Kondo effect, an impurity spin embedded in the Takhtajan-Babujian Heisenberg model and electron assisted-tunnelling of an atom in a double-well potential.
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The numerical solution of the Bethe ansatz equations of an integrable SU(2)-invariant generalization of the spin-S antiferromagnetic Heisenberg chain (Takhtajian-Babujian model) with a spin-S' impurity in zero magnetic field is presented. The entropy, specific heat and susceptibility of an impurity of spin S' are obtained numerically as a function of the spin S of the chain. Three situations have to be distinguished: (i) if S'=S the impurity just corresponds to one more site in the chain; (ii) if S'>S the impurity spin is only partially compensated (undercompensated) at T=0, leaving an effective spin of (S'-S); (iii) if S'
An impurity of spin S′=1/2 is introduced in the Babujian-Takhtajian Heisenberg model of spin S in one dimension. The impurity is located on the mth link of the chain and interacts with both neighboring sites. The interaction between impurity and Heisenberg chain is of a special type so that the integrability is preserved. The diagonalization of the transfer matrices leads to the Bethe ansatz equations of the model. The thermodynamics of the system is studied. For ferromagnetic coupling in the Heisenberg chain, the impurity is locked into the critical behavior of the lattice, i.e., at low temperatures the specific heat is proportional to T1/2 (ferromagnetic magnons) and the susceptibility diverges as T−2 (with logarithmic corrections). For antiferromagnetic coupling and S =1/2 the impurity is just one more site in the chain. If S ≳1/2 the collective properties of impurity and lattice give rise to critical behavior in complete analogy to the overcompensated n-channel Kondo problem. The zero-temperature entropy is finite in zero-field, but zero if the field is nonzero, giving rise to an essential singularity at T=H=0. As a consequence a two-peak structure arises in the specific heat in a small but finite field.
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