- Open Access
Comment on “Scaling and universality at noisy quench dynamical quantum phase transitions”
Phys. Rev. B 114, 206301 – Published 5 October, 2026
DOI: https://doi.org/10.1103/47dr-7f4r
Abstract
In [S. Ansari et al., Phys. Rev. B 112, 054304 (2025)], dynamical quantum phase transitions (DQPTs)—nonanalyticities in the Loschmidt return rate at critical times—are investigated in the presence of noise for a two-band model. The authors report that DQPTs persist even after averaging over the noise and they use their results to derive dynamical phase diagrams. The protocol used approximates the noise-averaged mixed state, obtained using a master equation, by a pure state, characterized by its excitation probability. In this comment we rigorously show that: (i) This approximation is exponentially poor in the thermodynamic limit. (ii) When using the correct metric, the Loschmidt echo of two density matrices in any two-dimensional Hilbert space can become zero if and only if both density matrices are pure, ruling out DQPTs for nonzero noise. (iii) An a posteriori reinterpretation of the results as an interferometric protocol is possible but such a protocol is unsuitable to investigate the effects of noise on DQPTs because it is inherently blind to decoherence. We also investigate alternative natural ways to average over noise realizations and show that in all of them DQPTs are smoothed out.
Physics Subject Headings (PhySH)
Comments & Replies
Reply to “Comment on ‘Scaling and universality at noisy quench dynamical quantum phase transitions’ ”
Article Text
Original Article
Scaling and universality at noisy quench dynamical quantum phase transitions
References (9)
- M. Heyl, A. Polkovnikov, and S. Kehrein, Dynamical quantum phase transitions in the transverse-field Ising model, Phys. Rev. Lett. 110, 135704 (2013).
- F. Andraschko and J. Sirker, Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach, Phys. Rev. B 89, 125120 (2014).
- M. Heyl, F. Pollmann, and B. Dóra, Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators, Phys. Rev. Lett. 121, 016801 (2018).
- A. Uhlmann, The “transition probability” in the state space of a*-algebra, Rep. Math. Phys. 9, 273 (1976).
- D. Bures, An extension of Kakutani s theorem on infinite product measures to the tensor product of semifinite w*-algebras, Trans. Am. Math. Soc. 135, 199 (1969).
- N. Sedlmayr, M. Fleischhauer, and J. Sirker, Fate of dynamical phase transitions at finite temperatures and in open systems, Phys. Rev. B 97, 045147 (2018).
- S. Ansari, R. Jafari, A. Akbari, and M. Abdi, Scaling and universality at noisy quench dynamical quantum phase transitions, Phys. Rev. B 112, 054304 (2025).
- M. Heyl and J. C. Budich, Dynamical topological quantum phase transitions for mixed states, Phys. Rev. B 96, 180304(R) (2017).
- U. Bhattacharya, S. Bandyopadhyay, and A. Dutta, Mixed state dynamical quantum phase transitions, Phys. Rev. B 96, 180303(R) (2017).
