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

TL;DR

This study provides numerical evidence that the frustrated $J_1$-$J_3$ quantum antiferromagnet on a square lattice exhibits a spin-Peierls (dimerized) ground state in an intermediate frustration regime, characterized by long-range dimer order.

Contribution

The paper identifies a spin-Peierls (dimerized) ground state in the $J_1$-$J_3$ model through numerical diagonalization, highlighting a novel phase in frustrated quantum antiferromagnets.

Findings

Incommensurate spin order is enhanced at larger $J_3/J_1$.

Short-range incommensurate order appears at intermediate $J_3/J_1$.

Evidence of long-range columnar dimer order in the intermediate regime.

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.