Most physical systems tend to order at a low enough temperature, and there are very few exceptions to this rule. For magnetic compounds, such exceptions are called "spin liquids" and over the last two decades, much effort has been made to characterize such states, which would not break any symmetry.
It is widely believed that a good caricature of a spin liquid is given by a short-range Valence Bond wave function, a linear superposition of all coverings of a given lattice by two-site singlets (valence bonds) :
One particular covering of the square lattice is shown in the figure, where arrows represent two-spin singlets . The intuition behind this wave-function is two-fold :
Researchers at LPT had already shown (Phys. Rev. B 82, 180408(R) (2010)) that this intuition fails on the square lattice, as the four-point (Valence-Bond Valence-Bond) correlations turn out to be quasi-long range ordered and, therefore, very close to cristallisation. But still no long-range order is present.
A recent Physical Review Letters studied this RVB wave function on the cubic lattice and showed the situation to be even more surprising. Large-scale Monte Carlo simulations revealed two unintuitive behaviors :
Further investigation is required to understand the generality of this new hybrid state of matter, which displays at once aspects of antiferromagnetism and of Coulomb physics.
To summarize, short-range Valence Bond wave functions (on bipartite lattices) are far from being featureless spin liquids !
Contact : Fabien Alet