Fate of the Higgs mode near quantum criticality

TL;DR

This study investigates the behavior of the Higgs mode near quantum criticality in 2+1 dimensional relativistic O(N) models, revealing a persistent Higgs peak and quantifying critical energy ratios through Monte Carlo simulations.

Contribution

It provides the first detailed Monte Carlo analysis of the Higgs mode near quantum critical points in 2+1 dimensions for N=2 and N=3.

Findings

The Higgs mode peak remains well-defined up to the critical point.

The fidelity of the Higgs peak is quantified.

Critical energy scale ratios are computed across the transition.

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.