Resonating-valence-bond physics is not always governed by the shortest tunneling loops

It is well known that the low-energy sector of quantum spin liquids and other magnetically disordered systems is governed by short-ranged resonating-valence bonds. Here we show that the standard minimal truncation to the nearest-neighbor valence-bond basis fails completely even for systems where it should work the most, according to received wisdom. This paradigm shift is demonstrated for the quantum spin-1/2 square kagome, where strong geometric frustration, similar to the kagome, prevents magnetic ordering down to zero temperature. The shortest tunneling events bear the strongest longer-range singlet fluctuations, leading to amplitudes that do not drop exponentially with the length of the loop L, and to an unexpected loop-six valence-bond crystal, which is otherwise very high in energy at the minimal truncation level. The low-energy effective description gives in addition a clear example of correlated loop processes that depend not only on the type of the loop but also on its lattice embedding, a direct manifestation of the long-range nature of the virtual singlets.