Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice

TL;DR

This study investigates the ground-state properties of the spin-half Heisenberg antiferromagnet on the star lattice, revealing a quantum paramagnetic ground state with potential magnetization plateaux and jumps, highlighting the effects of frustration and quantum fluctuations.

Contribution

It demonstrates that the star lattice is a second candidate among Archimedean lattices for quantum paramagnetism due to frustration and quantum fluctuations, with evidence of dimerization and magnetization phenomena.

Findings

Quantum paramagnetic ground state identified

Evidence of dimerization with a gap to excitations

Candidates for magnetization plateaux and jumps

Abstract

We study the ground-state properties of the spin-half Heisenberg antiferromagnet on the two-dimensional star lattice by spin-wave theory, exact diagonalization and a variational mean-field approach. We find evidence that the star lattice is (besides the \kagome lattice) a second candidate among the 11 uniform Archimedean lattices where quantum fluctuations in combination with frustration lead to a quantum paramagnetic ground state. Although the classical ground state of the Heisenberg antiferromagnet on the star exhibits a huge non-trivial degeneracy like on the \kagome lattice, its quantum ground state is most likely dimerized with a gap to all excitations. Finally, we find several candidates for plateaux in the magnetization curve as well as a macroscopic magnetization jump to saturation due to independent localized magnon states.