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

TL;DR

This paper proves that in noisy environments, dynamical quantum phase transitions cannot occur in mixed states, challenging previous claims that DQPTs persist under noise and showing they are smoothed out by averaging.

Contribution

It provides a rigorous proof that DQPTs are impossible in mixed states in two-dimensional Hilbert spaces, clarifying the effect of noise on DQPTs.

Findings

DQPTs only occur in pure states in 2D Hilbert spaces

Averaging over noise leads to mixed states where DQPTs are absent

Alternative averaging methods also eliminate DQPT signatures

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.