Numerical evidence for the spin-Peierls state in the frustrated quantum antiferromagnet

We study the spin-1/2 Heisenberg antiferromagnet with an antiferromagnetic J₃ (third-nearest-neighbor) interaction on a square lattice. We numerically diagonalize this ``J₁-J₃'' model on clusters up to 32 sites and search for ground-state properties as the frustration parameter J₃/J₁ changes. For ``larger'' J₃/J₁ we find enhancement of the incommensurate spin order, in agreement with various theoretical predictions. But for intermediate J₃/J₁, the low-lying excitation energy spectrum suggests that this incommensurate order is short range. Analysis of the ground-state expectation of the order parameter and the symmetries of the first excited state suggest that the spin-Peierls state is the best candidate for the ground state of the J₁-J₃ model in an intermediate J₃/J₁ region. {} 1996 The American Physical Society.