Amplitude (Higgs) mode at the superfluid-Mott glass transition

We investigate the amplitude (Higgs) mode of a diluted quantum rotor model in two and three space dimensions close to their respective superfluid-Mott glass quantum phase transitions [1,2]. After mapping the Hamiltonians onto appropriate classical XY models, the systems are simulated by means of large-scale Monte Carlo simulations. The scalar susceptibility of clean, undiluted systems exhibit sharp spectral peaks associated with the amplitude mode that show the expected scaling behavior close to the critical point. However, the diluted systems do not exhibit such sharp peaks. Instead, the scalar susceptibility is dominated by broad, non-critical peaks which obscure any potential amplitude mode. To understand the fate of the amplitude mode in diluted systems we study the localization behavior of the mode by calculating dispersion relations near the critical point, for varying dilution strengths. We also calculate conductivity as an indirect measure of the amplitude modes existence in diluted systems.

[1] Vojta, et. al., Phys. Rev. B, 94,134501 (2016)
[2] Crewse, et al., Phys. Rev. B, 98, 054514 (2018)