Spin-Peierls Dimerization of a s=1/2 Heisenberg Antiferromagnet on Square Lattice

TL;DR

This paper investigates the spin-Peierls dimerization in a square lattice Heisenberg antiferromagnet using unexpanded exchange couplings, revealing new energy behaviors and configurations that favor dimerization.

Contribution

It introduces a novel approach with unexpanded exchange couplings, showing different energy scaling laws and identifying the most energetically favorable dimerized configurations.

Findings

Columnar configuration has lower ground state energy than staggered.

Energy gain and gap increase faster in columnar configuration.

Power law behavior with logarithmic correction for energy and gap.

Abstract

Dimerization of a spin-half Heisenberg antiferromagnet on a square lattice is investigated by taking unexpanded exchange couplings. Several dimerized configurations are considered some of which are shown to have lower ground state energies than others. In particular, the lattice deformations resulting in alternate strong and weak couplings along both the principal axes of a square lattice are shown to result in a larger gain in energy. In addition, a `columnar' configuration is shown to have a lower ground state energy and a faster increase in the energy gap parameter than a `staggered' configuration. The inclusion of unexpanded exchange coupling leads to a power law behaviour for the magnetic energy gain and the spin-Peierls gap, which is qualitatively different from that reported earlier. Instead of varying as $\delta ^x$, the two quantities are shown proportional to $\delta ^\nu / |ln \delta|.$ It is thus proposed that the logarithmic correction, that was regarded as an outcome of including umklapp processes for small distortions, can also be a direct consequence of using an un-truncated spin-spin exchange interaction. The calculations, which employ the coupled cluster method, lead to a conclusion result that the dimerization of a spin-half Heisenberg antiferromagnet on a sqaure lattice is unconditional.