Orthogonality catastrophe and quantum speed limit for dynamical quantum phase transition

TL;DR

This paper explores the relationship between the orthogonality catastrophe and quantum speed limit in dynamical quantum phase transitions within the Creutz model, revealing how these concepts interplay near critical points and finite sizes.

Contribution

It demonstrates the existence of exact Loschmidt echo zeros in finite systems, analyzes the scaling of quantum speed limits, and proposes using quantum speed limits to detect static quantum critical points.

Findings

Exact zeros of Loschmidt echo can occur in finite systems.

Quantum speed limit times scale with system size and relate to the orthogonality catastrophe.

Quantum speed limit can serve as a detector for static quantum phase transitions.

Abstract

We investigate the orthogonality catastrophe and quantum speed limit in the Creutz model for dynamical quantum phase transitions. We demonstrate that exact zeros of the Loschmidt echo can exist in finite-size systems for specific discrete values. We highlight the role of the zero-energy mode when analyzing quench dynamics near the critical point. We also examine the behavior of the time for the first exact zeros of the Loschmidt echo and the corresponding quantum speed limit time as the system size increases. While the bound is not tight, it can be attributed to the scaling properties of the band gap and energy variance with respect to system size. As such, we establish a relation between the orthogonality catastrophe and quantum speed limit by referencing the full form of the Loschmidt echo. Significantly, we find the possibility of using the quantum speed limit to detect the critical point of a static quantum phase transition, along with a decrease in the amplitude of noise induced quantum speed limit.