The standard paradigm for describing critical phenomena is the Landau
paradigm of symmetry breaking, but it was proposed in the last decade
that so-called "exotic" or "de-confined" quantum critical points may
exist that lie outside this paradigm. However, despite extensive
theoretical work, the existence of such critical points in concrete
lattice Hamiltonians remained controversial: possible candidates exist
but the interpretation of the numerical data is in question. I'll talk
about recent work with Roger Melko and Sergei Isakov presenting strong
evidence for the existence of such a critical point, the so-called
XY^* point involving condensation of fractionalized particles carrying
conserved U(1) charge coupled to a Z_2 gauge theory. By a combination
of studying scaling of familiar quantities like the correlation
function (where we find a strongly nonclassical exponent) with
studying scaling of novel functions of the winding number distribution
(which directly probe topological properties of the discrete gauge
theory), we present "smoking gun" evidence for such a point in a
Bose-Hubbard model.