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-1/2 chain with both dimerization and frustration, i.e., an alternation \ensuremath{\delta} of the nearest-neighbor exchanges and a next-nearest-neighbor exchange ${\mathit{J}}_{2}$. For \ensuremath{\delta}=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 \ensuremath{\delta} to the power 0.667\ifmmode\pm\else\textpm\fi{}0.001. In the ${\mathit{J}}_{2}$-\ensuremath{\delta} plane, there is a disorder line 2${\mathit{J}}_{2}$+\ensuremath{\delta}=1. To the left of this line, the peak in the static structure factor S(q) is at ${\mathit{q}}_{\mathrm{max}}$=\ensuremath{\pi} (N\'eel phase), while to the right of the line, ${\mathit{q}}_{\mathrm{max}}$ decreases from \ensuremath{\pi} to \ensuremath{\pi}/2 as ${\mathit{J}}_{2}$ is increased to large values (spiral phase). For \ensuremath{\delta}=1, the system is equivalent to two coupled chains as on a ladder and it is gapped for all values of the interchain coupling.