A comparative study of the phase diagrams of spin-½ and spin-1 antiferromagnetic chains with dimerization and frustration

Abstract

The ground-state 'phase' diagrams and some low-energy properties of isotropic antiferromagnetic spin-½ and spin-1 chains with a next-nearest-neighbour exchange J₂ and an alternation δ of the nearest-neighbour exchanges have been compared for the first time using the density matrix renormalization group method. In the spin-½ chain, the system is gapless for δ=0 and J₂< J_2c=0.241, and is gapped everywhere else in the J₂-δplane. At J_2c , for small δ , the gap increases as δ^α, where α=0.667± 0.001.2J₂+δ=1 is a disorder line. To the left of this line, the structure factor S(q) peaks at q_max=π(the Neel 'phase'), while to the right q_max, decreases from π to π/2 (the spiral 'phase') as J₂increases. We also discover a '↑↑↓↓phase' for large values of both J₂and δ. In the spin-1 case, we find a line running from a gapless point at (J₂,δ)=(0,0.25±0.01) up to a 'gapless' point at (0.73±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-½ case, but the line ends at aboutδ=0.136. Similarly to the spin-½ case, to the left of this line, the peak in the structure factor is at π(the Neel 'phase'), while to the right of the line, it is at less than π(the spiral 'phase'). For δ=1, the system corresponds to a spin ladder and the system is gapped for all values of the interchain coupling for both spin-½ and spin-1 ladders.