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 $\hat{I}´$ of the nearest neighbor exchanges. We find a line running from a gapless point at $(J_2,\hat{I}´)=(0,0.25\pm 0.01)$ 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 $2J_2+\hat{I}´=1$ runs from $\hat{I}´=0$ to about $\hat{I}´=0.136$. To the left of this line, the peak in the structure factor $S(q)$ is at $\ddot{I}€$, while to the right of the line, it is at less than $\ddot{I}€$.

11 pages, plain TeX, 3 figures available on request