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arXiv:cond-mat/9808079 · Physical review. B, Condensed matter

Ghost spins and quantum critical behavior in a spin chain with local bond deformation

Jianhui Dai, Yupeng Wang, Ulrich Eckern

Published Sep 1, 1999• 8 citations
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Abstract

We study the impurity-induced critical behavior in an integrable $\mathrm{SU}(2)$-invariant model consisting of an open spin chain of arbitrary spin $S$ (Takhatajian-Babujian model) interacting with an impurity of spin ${S}^{\ensuremath{'}}$ located at one of the boundaries. For $S=1/2$ or ${S}^{\ensuremath{'}}=1/2,$ the impurity interaction takes a very simple form $J{S}_{1}\ensuremath{\cdot}{S}^{\ensuremath{'}}$ that describes the deformed boundary bond between the impurity ${S}^{\ensuremath{'}}$ and the first bulk spin ${S}_{1}$ with an arbitrary coupling strength $J.$ For a weak coupling $0<J<{J}_{0}/[{(S+S}^{\ensuremath{'}}{)}^{2}\ensuremath{-}1/4],$ the impurity is completely compensated, undercompensated, and overcompensated for ${S}^{\ensuremath{'}}=S,$ ${S}^{\ensuremath{'}}>S,$ and ${S}^{\ensuremath{'}}<S$ as in the usual Kondo problem. While for strong coupling $J>~{J}_{0}/[{(S+S}^{\ensuremath{'}}{)}^{2}\ensuremath{-}1/4],$ the impurity spin is split into two ghost spins. Their cooperative effect leads to a variety of new critical behaviors with different values of $|{S}^{\ensuremath{'}}\ensuremath{-}S|.$

DOI
10.1103/physrevb.60.6594

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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.