Comment on 'Revisiting the phase transitions of the Dicke model'

TL;DR

This paper critiques a recent study on the Dicke model, arguing that its key findings about phase transitions and chaos are artifacts of numerical truncation errors rather than intrinsic physical phenomena.

Contribution

It demonstrates that the purported upper energy bound and related results are spurious, caused by improper Hilbert space truncation in numerical simulations.

Findings

The upper bound energy $E_{*}$ is a numerical artifact.

Quantum chaos persists beyond the claimed energy bound.

Proper Hilbert space truncation removes the spurious effects.

Abstract

In the work of Das and Sharma [Phys. Rev. A 105, 033716 (2022)] the phase transitions of the Dicke model are studied. Its main result is that, besides the well-known quantum phase transition, excited-state quantum phase transition and thermal phase transition exhibited by the model, there exists an upper bound energy, $E_{*}$, beyond which the model ceases to exhibit quantum chaotic behavior and the structure of the eigenfunctions changes. Based on this finding, a number of well-established results about the Dicke model are called into question. We argue that this result and all its consequences are spurious numerical effects resulting from an improper truncation of the infinite-dimensional Hilbert space necessary for numerical diagonalization.