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-half 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. PACS numbers: 75.10.Jm, 75.50.Ee