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

TL;DR

This study uses the density matrix renormalization group method to analyze the $S=1$ antiferromagnetic spin chain with bond alternation, identifying a critical point with a continuous phase transition and edge state behavior.

Contribution

It provides the first detailed numerical analysis of the phase transition and edge states in the $S=1$ bond-alternated spin chain using DMRG.

Findings

Identified a massless point at δ_c = 0.25 ± 0.01.

Observed edge states for δ < δ_c that disappear for δ > δ_c.

Determined the spin wave velocity as 3.66 ± 0.10 and central charge as 1.0 ± 0.15 at the critical point.

Abstract

We study the $S=1$ quantum spin chain with bond alternation ${\cal H}=\sum _i (1-(-1)^i\delta)\vect{S}_i\cdot \vect{S}_{i+1}$ 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.