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

TL;DR

This study maps the phase diagram of a spin-1 antiferromagnetic chain with dimerization and frustration, revealing gapless points, degeneracy changes, and shifts in magnetic structure factors using the density matrix renormalization group method.

Contribution

It provides the first detailed phase diagram of the spin-1 chain with both dimerization and frustration, identifying critical lines and ground state degeneracies.

Findings

Identified a line from a gapless point to an almost gapless point in the phase diagram.

Discovered a disorder line where the peak of the structure factor shifts from  to less than .

Determined the degeneracy of the ground state varies across the phase diagram.

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