Ground state properties of a fully frustrated quantum spin system

TL;DR

This paper presents exact results on the ground state properties of a frustrated quantum spin system, revealing singlet states, zero magnetization, and susceptibility bounds, with implications for understanding complex magnetic materials.

Contribution

It provides the first exact analytical results for the ground states of a frustrated quantum spin system, using positive matrix representations and extending to other lattices.

Findings

Ground states are singlets and expressible via positive matrices.

Zero magnetization at zero external field for each tetrahedral unit.

An upper bound of 1/8 on susceptibility in natural units.

Abstract

We find that ground states of the quantum Heisenberg antiferromagnet on the geometrically frustrated pyrochlore checkerboard lattice are singlets and can be expressed in terms of positive matrices. The magnetization at zero external field vanishes for each frustrated tetrahedral unit separately and there is an upper bound of 1/8 in natural units on the susceptibility both for the ground state and at finite temperature. These results are the first exact ones in this field and generalize to some other lattices; the approach is also of interest for other spin systems.