A comparative study of the phase diagrams of spin-1/2 and spin-1 antiferromagnetic chains with dimerization and frustration

The ground-state ‘phase’ diagrams and some low-energy properties of isotropic antiferromagnetic spin- 1/2 and spin-1 chains with a next-nearest-neighbour exchange $J_2$ and an alternation $\delta$ of the nearest-neighbour exchanges have been compared for the first time using the density matrix renormalization group method. In the spin- 1/2 chain, the system is gapless for $\delta=0$ and $J_2 < J_{2c} = 0.241$, and is gapped everywhere else in the $J_2–\delta$ plane. At $J_{2c}$, for small $\delta$, the gap increases as $\delta^\{alpha}$, where $\alpha = 0.667 \pm 0.001. 2J_2 + \delta = 1$ is a disorder line. To the left of this line, the structure factor S(q) peaks at $q_{max}=\pi$ (the N´eel ‘phase’), while to the right, $q_{max}$ decreases from $\pi$ to $\pi/2$ (the spiral ‘phase’) as $J_2$ increases. We also discovera '$\uparrow\uparrow\downarrow\downarrow$ phase’ for large values of both $J_2$ and $\delta$. In the spin-1 case, we find a line running from a gapless point at $(J_2,\delta) = (0,0.25 \pm 0.01)$ up to a ‘gapless’ point at $(0.73 \pm 0.005, 0)$ such that the open-chain ground state is fourfold degenerate below the line and is unique above it. There is a disorder line in this case also and it has the same equation as in the spin- 1/2 case, but the line ends at about $\delta = 0.136$. Similarly to the spin- 1/2 case, to the left of this line, the peak in the structure factor is at $\pi$ (the N´eel ‘phase’), while to the right of the line, it is at less than $\pi$ (the spiral ‘phase’). For $\delta = 1$, the system corresponds to a spin ladder and the system is gapped for all values of the interchain coupling for both spin- 1/2 and spin-1 ladders