Sprecher
Beschreibung
When quantum fluctuations meet an extensive classical degeneracy, exotic strongly correlated states can arise. Paradigmatic examples are resonating valence bond (RVB) states of hard dimers. They are defined as equal weight quantum superpositions of all dimer coverings with one dimer entering each vertex of a lattice. In this work, we consider RVB states of hard trimers (tRVB), which are objects made up of two nearest-neighbor edges of a lattice that cannot share a common vertex. On certain lattices, tRVB states are known to be gapped and to possess a form of topological order with emergent $Z_3$ gauge symmetry, and thus to be good representatives of a quantum phase with $Z_3$ topological order. Here, we identify a necessary condition for having a gapped tRVB state with $Z_3$ topological order, similar to the condition of non-bipartite lattices for dimer models. Moreover, we propose and analyze a possible implementation of the trimer constraint in an array of Rydberg atoms.
