Fate of the Higgs mode near quantum criticality

Abstract

We study the relativistic O(N) field theory near the quantum critical point in 2+1 dimensions for N=2 and N=3. The scalar susceptibility is evaluated by Monte Carlo simulation. We show that the spectrum contains a peak associated with the Higgs mode, which remains well-defined all the way to the critical point. The fidelity of this peak and the amplitude ratio between the critical energy scales on both sides of the transition are computed.

6 pages, 5 figures, published version, relaxed estimation of the Higgs mass, added a supplementary information section on the analytic continuation method