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arXiv:cond-mat/9802163 · Physical review. B, Condensed matter

S=12 chain-boundary excitations in the Haldane phase of one-dimensional S=1 systems

Eric Polizzi, Frédéric Mila, Erik Schwartz Sørensen

Published Aug 1, 1998• 39 citations
arXivHTMLPDF

Abstract

The $S=\frac{1}{2}$ chain-boundary excitations occurring in the Haldane phase of $S=1$ antiferromagnetic spin chains are investigated. The bilinear-biquadratic Hamiltonian is used to study these excitations as a function of the strength of the biquadratic term, \ensuremath{\beta}, between $\ensuremath{-}1<~\ensuremath{\beta}<~1.$ At the Affleck-Kennedy-Lieb-Tasaki point, $\ensuremath{\beta}=\ensuremath{-}\frac{1}{3},$ we show explicitly that these excitations are localized at the boundaries of the chain on a length scale equal to the correlation length $\ensuremath{\xi}=1/\mathrm{ln}3$, and that the on-site magnetization for the first site is $〈{S}_{1}^{z}〉=\frac{2}{3}.$ Applying the density matrix renormalization group we show that the chain-boundary excitations remain localized at the boundaries for $\ensuremath{-}1<\ensuremath{\beta}<1.$ As the two critical points \ensuremath{\beta}=\ifmmode\pm\else\textpm\fi{}1 are approached the size of the $S=\frac{1}{2}$ objects diverges and their amplitude appears to vanish.

DOI
10.1103/physrevb.58.2407

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