Nonequilibrium probes of amplitude modes in quantum magnets

A spontaneously broken continuous symmetry results in collective modes in the excitation spectrum; in addition to the massless Goldstone modes, an amplitude (Higgs) mode is sometimes expected at finite energy. The stability of the Higgs mode in the vicinity of a quantum critical point (QCP) has been extensively debated for O(N) field theories for N=2,3. Interestingly, recent experiments on a two-dimensional Rydberg atom array, which is described by an N=1-component (Ising) theory, have observed collective long-lived oscillations of the order parameter, suggestive of an emergent Higgs mode. Motivated by these developments, we investigate the existence of a well-defined Higgs resonance at the QCP in a d-dimensional N=1 system—either in equilibrium or following a ramp to the QCP—by computing its (finite-temperature) spectral functions and scalar susceptibility for d=1,2. We also extend this analysis to quench spectroscopy of a d=1, N=2 model, examining the possibility of emergent collective modes beyond the scope of linear response.