The low-energy theory for the Bose-Hubbard model and the normal ground state of bosons

A bosonic realization of the SU(2) Lie algebra and of its vector representation is constructed, and an effective low-energy description of the Bose-Hubbard model in the form of anisotropic theory of quantum rotors is proposed and discussed. A possibility of a normal zero-temperature bosonic phase with neither crystalline nor superfluid order around the tip of the checkerboard-solid lobe at half-integer fillings is examined.