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Comment on "Role of Matter Interactions in Superradiant Phenomena"

Max Hörmann, Anja Langheld, Jonas Leibig, Andreas Schellenberger, Kai Phillip Schmidt

TL;DR

This paper addresses a discrepancy between Mendonça et al.'s Dicke-Ising phase diagram and established numerical and analytical results. It shows that an intermediate AFM-S phase and a change in the transition order for ferromagnetic Ising couplings exist within the same parameter range, using quantum Monte Carlo data from Langheld et al. and exact analyses in the thermodynamic limit. The key contributions are the explicit identification of the AFM-S phase in one dimension and the first-order ferromagnetic transition with a multi-critical point. The work emphasizes the importance of system size and resolution in numerically characterizing light-matter composites and provides guidance for validating new numerical approaches.

Abstract

Recently, Mendonça et al. [arXiv:2503.04961] investigated the Dicke-XXZ model and the Dicke-Ising model. For the latter model, their calculated quantum phase diagram contradicts claims about the existence of an intermediate phase with superradiant and antiferromagnetic order and the change in order of some phase transition lines, observed in other studies. In this comment we demonstrate that both features are indeed present in the Dicke-Ising model for the investigated parameter range in [arXiv:2503.04961].

Comment on "Role of Matter Interactions in Superradiant Phenomena"

TL;DR

This paper addresses a discrepancy between Mendonça et al.'s Dicke-Ising phase diagram and established numerical and analytical results. It shows that an intermediate AFM-S phase and a change in the transition order for ferromagnetic Ising couplings exist within the same parameter range, using quantum Monte Carlo data from Langheld et al. and exact analyses in the thermodynamic limit. The key contributions are the explicit identification of the AFM-S phase in one dimension and the first-order ferromagnetic transition with a multi-critical point. The work emphasizes the importance of system size and resolution in numerically characterizing light-matter composites and provides guidance for validating new numerical approaches.

Abstract

Recently, Mendonça et al. [arXiv:2503.04961] investigated the Dicke-XXZ model and the Dicke-Ising model. For the latter model, their calculated quantum phase diagram contradicts claims about the existence of an intermediate phase with superradiant and antiferromagnetic order and the change in order of some phase transition lines, observed in other studies. In this comment we demonstrate that both features are indeed present in the Dicke-Ising model for the investigated parameter range in [arXiv:2503.04961].

Paper Structure

This paper contains 4 sections, 1 equation, 1 figure.

Table of Contents

  1. Introduction
  2. On the intermediate antiferromagnetic superradiant phase
  3. On the order of phase transitions for ferromagnetic Ising interactions
  4. Conclusions

Figures (1)

  • Figure 1: Phase diagram of the Dicke-Ising model, choosing $\omega=\varepsilon=1$ and similar parameter ranges for $g,J$ as in Fig. 3(c) from Ref. Mendonca2025. Crosses and background colors show the QMC results using the algorithm from Ref. Langheld2024a, black lines depict the mean-field results Zhang2014Schellenberger2024. The black mean-field lines fade when they start to deviate from the QMC analysis. (a) Full phase diagram containing antiferromagnetic normal (AFM-N), antiferromagnetic superradiant (AFM-S), paramagnetic normal (PM-N), and paramagnetic superradiant (PM-S) phases, (b) Zoom into intermediate AFM-S phase, which was not found by Ref. Mendonca2025, (c) Zoom into emerging deviation from mean-field results Zhang2014Schellenberger2024 for ferromagnetic Ising interactions not included in Ref. Mendonca2025.