Seminar "Resonating valence bond physics is not always governed by the shortest tunnelling loops" by Arnaud Ralko

Resonating valence bond physics is not always governed by the shortest tunnelling 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 (RVB). In this talk, I will show that the standard minimal truncation to the nearest-neighbor valence bond (NNVB) 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 (VBC), 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.