Universal Properties of the Higgs Resonance in (2+1)-Dimensional U(1) Critical Systems

TL;DR

This paper investigates the universal spectral properties of the Higgs resonance in (2+1)-dimensional U(1) critical systems, revealing a sharp low-frequency resonance across different phases through Monte Carlo simulations.

Contribution

It provides the first detailed analysis of the Higgs resonance in (2+1)D U(1) critical systems, highlighting universal features and collective modes in strongly coupled relativistic field theories.

Findings

Universal low-frequency resonance observed in spectral functions.

Resonance is sharp in superfluid and Mott insulator phases.

Damped oscillations follow the resonance before saturation.

Abstract

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 low-frequency 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. The counterintuitive resonance feature in the insulating and normal phases calls for deeper understanding of collective modes in the strongly coupled (2+1)-dimensional relativistic field theory. Our results are derived from analytically continued correlation functions obtained from path-integral Monte Carlo simulations of the Bose-Hubbard model.