Phase Diagram of the Spin-One Heisenberg System with Dimerization and Frustration

Abstract

We use the density matrix renormalization group method to study the ground state properties of an antiferromagnetic spin-$1$ chain with a next-nearest neighbor exchange $J_2 ~$ and an alternation $δ$ of the nearest neighbor exchanges. We find a line running from a gapless point at $(J_2 , δ) = (0, 0.25 \pm 0.01)$ upto an almost gapless point at $(0.725 \pm 0.01, 0$ such that the open chain ground state is $4$-fold degenerate below the line and is unique above it. A disorder line $2 J_2 + δ= 1$ runs from $δ=0$ to about $δ=0.136$. To the left of this line, the peak in the structure factor $S(q)$ is at $π$, while to the right of the line, it is at less than $π$.