Roton minimum as fingerprint of magnon-Higgs scattering in ordered quantum antiferromagnets

TL;DR

This paper presents a comprehensive analysis of magnon behavior in quantum antiferromagnets, revealing that the high-energy roton minimum results from strong magnon-Higgs scattering, with implications for understanding magnetic excitations.

Contribution

It introduces a continuous similarity transformation approach to describe magnons across energy scales and identifies magnon-Higgs interactions as key to the roton minimum.

Findings

Magnon-magnon attraction induces a Higgs resonance.

High-energy roton minimum caused by magnon-Higgs scattering.

Method provides consistent magnon description from low to high energies.

Abstract

A quantitative description of magnons in long-range ordered quantum antiferromagnets is presented which is consistent from low to high energies. It is illustrated for the generic $S=1/2$ Heisenberg model on the square lattice. The approach is based on a continuous similarity transformation in momentum space using the scaling dimension as truncation criterion. Evidence is found for significant magnon-magnon attraction inducing a Higgs resonance. The high-energy roton minimum in the magnon dispersion appears to be induced by strong magnon-Higgs scattering.