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Journal of Applied Physics

Overcompensated impurities in antiferromagnetic Heisenberg chains

P. Schlottmann

Published Nov 15, 1991• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.350049

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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.
The authors consider an integrable SU(2)-invariant model consisting of the Heisenberg chain of arbitrary spin S (Takhtajan-Babujian model) interacting with an impurity of spin S'. The impurity is assumed to be located on the mth link of the chain and interacts only with both neighbouring sites. The starting point is a set of commuting transfer matrices, whose local weights satisfy triangular Yang-Baxter relations. The diagonalization of the transfer matrices leads to the Bethe ansatz equations for the model. The thermodynamics of the system is studied. 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 at T=0, leaving an effective spin of (S'-S). (iii) S'
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'
We construct an integrable SU(2)-invariant model consisting of the Heisenberg chain of spin 1 interacting with an impurity of spin S. This generalizes previous results by Andrei and Johannesson for the spin-(1/2 chain. The model Hamiltonian is diagonalized and the thermodynamics is obtained. For ferromagnetic coupling at low temperatures the impurity susceptibility diverges as ${T}^{\mathrm{\ensuremath{-}}2}$ and the impurity specific heat is proportional to T1/2{T}^{1/2}T1/2 for all values of the impurity spin S. For antiferromagnetic coupling and T=0 the impurity susceptibility diverges proportionally to \ensuremath{\Vert}lnH\ensuremath{\Vert} as H\ensuremath{\rightarrow}0 if S=(1/2, while if S>1 the impurity spin is only partially compensated for by the S=1 chain.
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 consider an integrable SU(2)-invariant model consisting of a Heisenberg chain of spins S (the Takhtajan-Babujian model) interacting with a finite concentration c of impurity spins S ´. The thermodynamic Bethe- ansatz equations are stated for this model. The ground-state equations are analysed as a function of c , the magnetic field and the coupling parameter (impurity rapidity p 0 ) of the impurities to the lattice. In zero field the ground state is a singlet for finite c , but becomes non-Fermi-liquid-like as c 0 for S ´< S . Two rapidity bands play a role at T = 0 corresponding to strings of length 2 S and 2 S ´, respectively. The van Hove singularities of the empty bands define two critical fields, H c ( c , p 0 ) and H s ( c , p 0 ), at which the susceptibility diverges. H c tends to zero as c 0 giving rise to a crossover from non-Fermi-liquid behaviour for H > H c to Fermi-liquid-like behaviour for H < H c . The spectrum of elementary excitations and the finite-size corrections to the ground-state energy are calculated, and used to discuss the asymptotic behaviour of spin-spin correlation functions for long times and large distances.
We study the low-temperature behavior of a boundary magnetic impurity ${S}^{\ensuremath{'}}=1/2$ in an open ferromagnetic Takhatajian-Babujian spin-SSS chain. For antiferromagnetic Kondo coupling, it is shown via the Bethe ansatz solution that the impurity spin is always locked into the critical behavior of the bulk. At low temperatures, a local composite of spin-$(S\ensuremath{-}1/2)$ forms near the impurity site and its contribution to specific heat is of simple power law T1/2.{T}^{1/2}.T1/2. The absence of the overscreened Kondo effect is due to the large correlation length of host spins which is divergent near the quantum critical point.