Density-matrix renormalization-group studies of the spin-1/2 Heisenberg system with dimerization and frustration

Using the density-matrix renormalization-group technique, we study the ground-state phase diagram and other low-energy properties of an isotropic antiferromagnetic spin-1/2 chain with both dimerization and frustration, i.e., an alternation {δ} of the nearest-neighbor exchanges and a next-nearest-neighbor exchange J₂. For {δ}=0, the system is gapless for J₂{J}2c$ and has a gap for ${J}₂$>${J}2c$ where ${J}2c$ is about 0.241. For ${J}₂$=${J}2c, the gap above the ground state grows as δ to the power 0.667±0.001. In the{J}₂-δ plane, there is a disorder line 2{J}₂+δ=1. To the left of this line, the peak in the static structure factor S(q) is at{q}ₘₐₓ=π (N\'eel phase), while to the right of the line,{q}ₘₐₓdecreases from π to π/2 as{J}₂$ is increased to large values (spiral phase). For {δ}=1, the system is equivalent to two coupled chains as on a ladder and it is gapped for all values of the interchain coupling.