Higgs amplitude mode in the vicinity of a $(2+1)$-dimensional quantum critical point: a nonperturbative renormalization-group approach

TL;DR

This paper investigates the Higgs amplitude mode near a quantum critical point in a 2+1 dimensional relativistic quantum O(N) model using a nonperturbative renormalization group approach, revealing the existence and properties of the Higgs resonance for specific N values.

Contribution

The study extends the nonperturbative renormalization group method to compute 4-point functions and characterizes the Higgs mode across different N values near a quantum critical point.

Findings

Higgs resonance is well-defined for N=2 and N=3 in the ordered phase.

No Higgs resonance is observed for N≥4.

In the disordered phase, the spectral function shows threshold behavior without a Higgs peak.

Abstract

We study the "Higgs" amplitude mode in the relativistic quantum O($N$) model in two space dimensions. Using the nonperturbative renormalization group and the Blaizot--M\'endez-Galain--Wschebor approximation (which we generalize to compute 4-point correlation functions), we compute the O($N$) invariant scalar susceptibility at zero temperature in the vicinity of the quantum critical point. In the ordered phase, we find a well-defined Higgs resonance for $N=2$ and $N=3$ and determine its universal properties. No resonance is found for $N\geq 4$. In the disordered phase, the spectral function exhibits a threshold behavior with no Higgs-like peak. We also show that for $N=2$ the Higgs mode manifests itself as a very broad peak in the longitudinal susceptibility in spite of the infrared divergence of the latter. We compare our findings with results from quantum Monte Carlo simulations and $\epsilon=4-(d+1)$ expansion near $d=3$.