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-½ 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< J2c and has a gap for J2> J2c where J2c is about 0.241. For J2=J2c, the gap above the ground state grows as δ to the power 0.667±0.001. In the J2-δ plane, there is a disorder line 2J2+δ=1. To the left of this line, the peak in the static structure factor S(q) is at qmax=π (Neel phase), while to the right of the line, qmax decreases from π to π/2 as J2 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