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$S=1/2$ Chain-Boundary Excitations in the Haldane Phase of 1D $S=1$ Systems

E. Polizzi·F. Mila·E. S. Sorensen
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Abstract

The $s=1/2$ chain-boundary excitations occurring in the Haldane phaseof $s=1$ 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, $β$, between $-1\leβ\le1$. At the AKLT point, $β=-1/3$, we show explicitly that these excitations are localized at the boundaries of the chain on a length scale equal to the correlation length $ξ=1/\ln 3$, and that the on-site magnetization for the first site is $ =2/3$. Applying the density matrixrenormalization group we show that the chain-boundaryexcitations remain localized at the boundaries for $-1\leβ\le1$. As the two critical points $β=\pm1$ are approached the size of the $s=1/2$ objects diverges and their amplitude vanishes.

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E. Polizzi, F. Mila, E. S. Sorensen. 1998-02-15. $S=1/2$ Chain-Boundary Excitations in the Haldane Phase of 1D $S=1$ Systems. https://doi.org/10.1103/physrevb.58.2407

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