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arXiv:cond-mat/0212199 · APS March Meeting Abstracts

Doped dimerized spin chains: Another path to superconductivity

Alexander Seidel, Patrick A. Lee

Published Dec 9, 2002• 0 citations
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Abstract

This paper has been withdrawn by the authors, since we have come to believe that the present approach is not convergent at small doping. We will shortly submit an improved theory of the tJJ' model at small J/t in the dilute hole limit. This will be a new submission will go by a different submission number.
DOI
10.48550/arxiv.cond-mat/0212199

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We study the one-dimensional $t\ensuremath{-}J\ensuremath{-}{J}^{\ensuremath{'}}$-model in the limit of small hole doping x and small J/t,J/t,J/t, ${J}^{\ensuremath{'}}/t.$ Special emphasis is put on the regime ${J}^{\ensuremath{'}}/J\ensuremath{\approx}0.5,$ where a spin gap is present at small doping and the undoped spin chain is strongly dimerized. Using a perturbative approach and Luttinger liquid arguments, we demonstrate for this nonintegrable class of models that the charge degrees of freedom behave as noninteracting spinless solitons in the dilute hole limit. Our approach is also used to evaluate the energy and mass renormalization of a single hole. Interestingly, the corrections of these quantities are in powers of J/t.\sqrt{J/t}.J/t​. At ${J}^{\ensuremath{'}}/J=0.5$ we construct a variational spin-polaron wave function for the hole and find good agreement with our perturbative results.
We reconsider some of the previous studies of the interactions between the holes and the spin background in the Hubbard model in the small-doping limit. We show that the hole-hole interaction due to the transverse magnetization fluctuations (i.e., spin waves) is finite at arbitrarily small hole density. It may be comparable to the coupling due to the longitudinal magnetization fluctuations (which are the essence of the ``spin-bag'' mechanism of Schrieffer, Wen, and Zhang). This suggests that the two couplings should be considered simultaneously when studying the phase diagram of the lightly doped quantum antiferromagnets at the values of U/t relevant to the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconducting materials. We also show that in the large-(U/t) limit the Hubbard-model expressions for the coupling of holes reduce to those given by Shraiman and Siggia for the t-J model. This provides a link between the weak- and the strong-coupling theories of the doped quantum antiferromagnets, in the small-doping limit.