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Published online by Cambridge University Press: 05 March 2013
In the last chapter we introduced the concept of valence-bond states and discussed several quantum disordered phases in this language. Here we will see that the quantum fluctuations of valence-bond systems are best captured in terms of a much simpler effective theory, the quantum-dimer models. An understanding of these types of phases is best accomplished in terms of gauge theories. The phases of gauge theories and their topological properties will allow us to introduce the concept of a topological phase of matter in a precise way.
Fluctuations of valence bonds: quantum-dimer models
The valence-bond crystal of Section 8.5 has a spin-correlation length of the order of one lattice constant. It represents a quantum paramagnet. However, it is not a translationally invariant state, unlike the equal-amplitude short-range RVB state. It has crystalline order of its valence bonds and it is a four-fold degenerate state.
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