Elliott H. Lieb, Peter Schupp
Ground state properties of a fully frustrated quantum spin system
(29K, revtex)

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.