Wave Permanent Functions for Featureless Bosonic Mott Insulators on the 1/3-Filled Kagome Lattice

We study Bose-Hubbard models on tight-binding, non-Bravais lattices, with a filling of one boson per unit cell—and thus fractional site filling. We discuss situations where no classical bosonic insulator, which is a product state of particles on independent sites, is admitted. Nevertheless, we show that it is possible to construct a quantum Mott insulator of bosons if a trivial band insulator of fermions is possible at the same filling. The ground state wave function is simply a permanent of exponentially localized Wannier orbitals. Such a Wannier permanent wave function is featureless in that it respects all lattice symmetries and is the unique ground state of a parent Hamiltonian that we construct. Motivated by the recent experimental demonstration of a kagome optical lattice of bosons, we study this lattice at 1/3 site filling. Previous approaches to this problem have invariably produced either broken-symmetry states or topological order. Surprisingly, we demonstrate that a featureless insulator is a possible alternative and is the exact ground state of a local Hamiltonian. We briefly comment on the experimental relevance of our results to ultracold atoms as well as to 1/3 magnetization plateaus for kagome spin models in an applied field.