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

P. W. Leung·Ngar-wing Lam
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Abstract

We study the spin-$1\over2$ Heisenberg antiferromagnet with an antiferromagnetic $J_3$ (third nearest neighbor) interaction on a square lattice. We numerically diagonalize this ``$J_1$-$J_3$'' model on clusters up to 32-sites and search for novel ground state properties as the frustration parameter $J_3/J_1$ changes. For ``larger'' $J_3/J_1$ we find enhancement of incommensurate spin order, in agreement with spin-wave, large-$N$ expansions, and other predictions. But for intermediate $J_3/J_1$, the low lying excitation energy spectrum suggests that this incommensurate order is short-range. In the same region, the first excited state has the symmetries of the columnar dimer (spin-Peierls) state. The columnar dimer order parameter suggests the presence of long-range columnar dimer order. Hence, this spin-Peierls state is the best candidate for the ground state of the $J_1$-$J_3$ model in an intermediate $J_3/J_1$ region.

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P. W. Leung, Ngar-wing Lam. 1995-08-01. Numerical evidence for the spin-Peierls state in the frustrated quantum antiferromagnet. https://doi.org/10.1103/physrevb.53.2213

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