Numerical Study of the $S=1$ Antiferrromagnetic Spin Chain with Bond Alternation

Abstract

We study the $S=1$ quantum spin chain with bond alternation ${\cal H}=\sum _i (1-(-1)^iδ)\vect{S}_i\cdot \vect{S}_{i+1}$ by the density matrix renormalization group method recently proposed by Steven R. White (\PRL{69}{3844}{1993}). We find a massless point at ${\delta }_c=0.25\pm 0.01$. We also find the edge states in the region $\delta <{\delta }_c$ under the open boundary condition, which disappear in the region $\delta >{\delta }_c$. At the massless point, the spin wave velocity $v_s$ is $3.66\pm 0.10$ and the central charge $c$ is $1.0\pm 0.15$. Our results indicate that a continuous phase transition occurs at the massless point $\delta ={\delta }_c$ accompanying breaking of the hidden $Z_2\times Z_2$ symmetry.

9 pages and 1 PostScript figure, Revtex 3.0 (Minor corrections in TEX-file format to remove possible compilatory troubles.)

References in corpus (1)

• Large-Scale Numerical Evidence for Bose Condensation in the S=1 Antiferromagnetic Chain in a Strong Field

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