Minimal Models of Frustrated Quantum Magnets

Frustrated quantum magnets are a real challenge to theorists because standard analytical and numerical methods fail in most cases. Significant progress has been recently achieved however on the basis of what one may call minimal models, i.e. models which keep at least one important aspect of frustration, but which are otherwise simple enough to be understood. In this paper, I will concentrate on two types of minimal models, Quantum Dimer Models and hard‐core boson models. In the case of Quantum Dimer Models, I will review the evidence in favour of a Resonating Valence Bond (RVB) spin‐liquid phase, and I will discuss under which circumstances such models might be good effective models. For hard‐core boson models, which have been successfully used for quite some time for ladders and other non‐frustrated models of coupled dimers, I will describe the specificities introduced by frustration (reduced kinetic energy, correlated hopping,…) and the unexpected properties they induce.