Valence-bond-solid order in antiferromagnets with spin-lattice coupling

TL;DR

This paper demonstrates that spin-lattice coupling can stabilize a valence-bond-solid order in two-dimensional antiferromagnets, even when the spin and lattice parameters are not commensurate, leading to unique excitation spectra.

Contribution

It introduces a novel mechanism for VBS order stabilization via spin-lattice coupling in non-commensurate systems, expanding understanding beyond traditional AKLT models.

Findings

VBS order can be stabilized by spin-lattice coupling in non-commensurate systems.

Ground state exhibits a $\

sqrt{3} imes ext{ } ext{sqrt{3}}$ modulation of valence bonds.

Abstract

We propose that a valence-bond-solid (VBS) order can be stabilized in certain two-dimensional antiferromagnets due to spin-lattice coupling. In contrast to the VBS state of the Affleck-Kennedy-Lieb-Tesaki (AKLT) type in which the spin $2S$ and the lattice coordination $z$ must be commensurate, the spin-lattice coupling-induced VBS state can occur when $2S$ is not an integer multiple of $z$. As a concrete example, S=2 spins on the triangular network with $z=6$ is discussed. Within the Schwinger boson mean-field theory it is shown that the ground state is given by the $\sqrt{3}\times\sqrt{3}$ modulation of the valence bond amplitudes for sufficiently strong spin-lattice coupling. Using the corresponding AKLT wave function, we work out the excitation spectrum for this state within the single-mode approximation. The calculated spectrum should provide a new type of collective mode which is distinct from the spin wave excitations of the magnetically ordered ground state.