Competing Orders and Non-Landau-Ginzburg-Wilson Criticality in (Bose) Mott Transitions

This paper reviews a recent non-Landau-Ginzburg-Wilson (LGW) approach to superfluid to Mott insulator transitions in two dimensional bosonic lattice systems, using a dual vortex field theory [L. Balents, L. Bartosch, A. Burkov, S. Sachdev and K. Sengupta, Phys. Rev. B 71 (2005), 144508; Phys. Rev. B 71 (2005), 144509]. The physical interpretation of conventional LGW theory of quantum criticality is re-examined and similarities and differences with the vortex picture are discussed. The ``unification'' of various competing (insulating) orders, and the coincidence of these orders with the Mott transition are readily understood formulation. Some aspects of the recent theory of ``deconfined'' quantum criticality, which are to an extent subsumed approach, are discussed. A pedagogical presentation of the ``nuts and bolts'' of boson-vortex duality at the hamiltonian level is included, tailored to a condensed matter audience.