DMRG Studies of the Spin-Half 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-half chain with both dimerization and frustration, i.e., an alternation $δ$ of the nearest neighbor exchanges and a next-nearest-neighbor exchange $J_2~$. For $δ= 0$, the system is gapless for $J_2 < J_{2c} ~$ 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 $0.667 \pm 0.001$. 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 $q_{max} = π$ (Neel phase), while to the right of the line, $q_{max}$ decreases 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.