Path Integral Approach to Geometrically Frustrated Quantum Antiferromagnets

We develop a path integral approach to geometrically frustrated quantum antiferromagnets. Using Hubbard--Stratonovich transformations to decouple the interactions within clusters of spins, we establish a high temperature expansion of the quantum partition function. This semiclassical approach based on conjugate cluster variables allows us to descend below the Curie--Weiss temperature scale, and to describe the emergent spin liquid regime. We make contact with complementary approaches based on spin wave theory.