Criticality in the 2+1-dimensional compact Higgs model and fractionalized insulators

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We use a novel method of computing the third moment M₃ of the action of the 2+1-dimensional compact Higgs model in the adjoint representation with q=2 to extract correlation length and specific heat exponents nu and alpha, without invoking hyperscaling. Finite-size scaling analysis of M₃ yields the ratio (1+alpha)/nu and 1/nu separately. We find that alpha and nu vary along the critical line of the theory, which however exhibits a remarkable resilience of Z₂ criticality. We propose this novel universality class to be that of the quantum phase transition from a Mott-Hubbard insulator to a charge-fractionalized insulator in two spatial dimensions.