Comment on: "Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions"

TL;DR

This work addresses whether dynamical quantum phase transitions (DQPTs) persist when a noisy ramp drives a two-band system. The authors prove two general results: (1) noise averaging drives the system into a mixed state in any two-dimensional Hilbert space, and (2) in 2D a Loschmidt echo can vanish only if both states are pure, implying no DQPTs under the noise-averaging procedure used in prior work. They further show that using a pure-state approximation for the mixed initial state is both non-optimal and exponentially inaccurate in system size, and they analyze three natural noise-averaging schemes, all of which fail to produce non-analytic DQPTs: either the mixed-state Loschmidt rate remains smooth, or the unitary realizations’ cusps do not align coherently across realizations. The results reconcile the fate of DQPTs with expectations from dissipation and finite-temperature effects, demonstrating that noise averaging generally destroys DQPTs in the two-band, translationally invariant setting. Overall, the work corrects the record on Ansari25’s claims and clarifies the fragility of DQPTs to noise, with implications for dynamical phase diagrams in realistic, noisy quantum systems.

Abstract

In Ref. Ansari et al., dynamical quantum phase transitions (DQPTs) -- non-analyticities 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. In this comment we rigorously prove that in any two-dimensional Hilbert space the Loschmidt echo of two density matrices can only become zero if and only if both density matrices are pure. As a consequence, the existence of DQPTs in the considered scenario is strictly ruled out for non-zero noise because the considered averaging leads to a mixed state. We also investigate alternative natural ways to average over noise realizations and show that in all of them DQPTs are smoothed out.