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

Abstract

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< J_2c and has a gap for J₂> J_2c where J_2c is about 0.241. For J₂=J_2c, 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 q_max=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.