Critical liquid phases for frustrated bosons in two dimensions

An interesting question in strongly correlated systems is the possibility of a ``metallic'' bosonic liquid -- a quantum liquid phase of bosons that is neither superfluid nor Mott insulator. We present an attempt to construct such states using slave particle technique borrowed from theories of spin liquids; the approach can be also loosely viewed as a flux attachment treatment performed in the absence of time reversal breaking. We describe properties of thus constructed boson liquid states, which support gapless boson excitations residing on ``Bose surfaces'' in the momentum space and exhibit power law correlations in various properties. We also suggest a promising model Hamiltonian of hard-core bosons hopping on a square lattice and with frustrating ring exchanges which may have such a phase.