Kun Chen, Longxiang Liu, Youjin Deng, Lode Pollet, Nikolay Prokof'ev
We present spectral functions for the magnitude squared of the order parameter in the scaling limit of the two-dimensional superfluid to Mott insulator quantum phase transition at constant density, which has emergent particle-hole symmetry and Lorentz invariance. The universal functions for the superfluid, Mott insulator, and normal liquid phases reveal a Higgs resonance which is relatively sharp and is followed by a damped oscillation (in the first two phases only) before saturating to the quantum critical plateau. In order to understand the counter-intuitive Higgs resonance in the insulating and normal phases, we invoke a picture of a scale-dependent Mexican hat. Our results are derived from analytically continued correlation functions obtained from path-integral Monte Carlo simulations of the Bose-Hubbard model.
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http://arxiv.org/abs/1301.3139
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