Topological ice-rule phase of bosons in the Cairo Pentagonal lattice

4 pages, 5 figuresThe low temperature phase diagram of the extended hard-core boson Hubbard model on the Cairo Pentagonal lattice is presented. We provide an extensive numerical study by using a stochastic series expansion quantum Monte Carlo and a cluster mean field theory. The complex connectivity enhances the frustration and leads to unconventional phases such as a 1/3-ferrimagnetic plateau stabilized by quantum fluctuations. More particularly, we identify a 5/12-topological phase due to the presence of a specific local ice-rule constraint. Thermal fluctuations, sign of the hopping (frustration) and isotropy of the chemical potential are also discussed