Frustrated spin-1/2 model in two dimensions with columnar dimer states as possible ground states.

Abstract

An antiferromagnetic spin S=1/2 model, the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$-${\mathit{J}}_{3}$-${\mathit{J}}_{4}$-${\mathit{J}}_{5}$ model, is considered in two dimensions. ${\mathit{J}}_{1}$,${\mathit{J}}_{2}$,${\mathit{J}}_{3}$,${\mathit{J}}_{4}$,${\mathit{J}}_{5}$ are the strengths of the nearest-neighbor, diagonal, next-nearest-neighbor, knight's-move-distance-away, and further-neighbor-diagonal interactions, respectively. It is known that when ${\mathit{J}}_{1}$:${\mathit{J}}_{2}$:${\mathit{J}}_{3}$:${\mathit{J}}_{4}$:${\mathit{J}}_{5}$=1:1:1/2:1/2:1/4 the four columnar dimer states are the exact eigenstates. In a bosonic mean-field theory, we find that the columnar dimer state is the ground state. We compare the results obtained with those obtained in the same mean-field theory for the one-dimensional Majumdar-Ghosh (MG) model. For special values of the couplings, the dimer state is known to be the exact ground state of the MG model. The comparison of the mean-field results for both the models leads to the conjecture that the columnar dimer states are the exact ground states of the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$-${\mathit{J}}_{3}$-${\mathit{J}}_{4}$-${\mathit{J}}_{5}$ model.