# Stable high-temperature paramagnons in a three-dimensional antiferromagnet near quantum criticality: Application to TlCuCl$_3$

## TL;DR

This paper explains the stability and high-temperature behavior of paramagnons in a three-dimensional antiferromagnet near quantum criticality, specifically applied to TlCuCl$_3$, using a thermal renormalization group approach.

## Contribution

It introduces a mechanism involving thermal mass scale emergence and multi-magnon interaction renormalization to explain experimental observations in TlCuCl$_3$.

## Key findings

- Paramagnons remain stable up to high temperatures with high thermal damping.
- Width to mass ratios of paramagnons match those of the amplitude mode.
- The theoretical model agrees quantitatively with experimental data.

## Abstract

The complete set of hallmarks of the three-dimensional antiferromagnet near the quantum critical point has been recently observed in the spin dimer compound TlCuCl$_3$. Nonetheless, the mechanism, responsible for several distinct features of the experimental data, has remained a puzzle, namely: (i) the paramagnons exhibit remarkable robustness to thermal damping and are stable up to high temperatures, where $k_B T$ is comparable with the excitation energy, (ii) the width to mass ratios of the high-temperature paramagnons are, within the error bars, equal to that of the low-temperature amplitude (or Higgs) mode. We propose such a mechanism and identify two principal factors, contributing to the scaling between width to mass ratios of the paramagnon and the amplitude mode: (i) the emergence of the thermal mass scale reorganizing the paramagnon decay processes, and (ii) substantial renormalization of the multi-magnon interactions by thermal fluctuations. The study is carried out for the general case of a $D= 3 + 1$ quantum antiferromagnet within the framework of the $\varphi^4$ model using the hybrid Callan-Symanzik + Wilson thermal renormalization group method. Our approach is tested by demonstrating a good quantitative agreement with available experimental data across the phase diagram of TlCuCl$_3$.