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 ${\mathit{J}}_2$. For δ=0, the system is gapless for ${\mathit{J}}_2$<${\mathit{J}}_{2\mathit{c}}$ and has a gap for ${\mathit{J}}_2$>${\mathit{J}}_{2\mathit{c}}$ where ${\mathit{J}}_{2\mathit{c}}$ is about 0.241. For ${\mathit{J}}_2$=${\mathit{J}}_{2\mathit{c}}$, the gap above the ground state grows as δ to the power 0.667±0.001. In the ${\mathit{J}}_2$-δ plane, there is a disorder line 2${\mathit{J}}_2$+δ=1. To the left of this line, the peak in the static structure factor S(q) is at ${\mathit{q}}_{\max }$=π (Néel phase), while to the right of the line, ${\mathit{q}}_{\max }$ decreases from π to π/2 as ${\mathit{J}}_2$ 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.