Exact zeros of the Loschmidt echo and quantum speed limit time for the dynamical quantum phase transition in finite-size systems

TL;DR

This paper investigates the occurrence of exact zeros in the Loschmidt echo and quantum speed limit time during dynamical quantum phase transitions in finite systems, revealing their dependence on system size and initial phase.

Contribution

It provides a detailed analysis of how exact zeros and quantum speed limit times behave in finite and infinite systems, highlighting the discrete and continuous nature of parameters involved.

Findings

Exact zeros exist in finite systems at specific discrete parameters.

Quantum speed limit time scales linearly with system size.

Behavior of minimal quantum speed limit time depends on initial phase.

Abstract

We study exact zeros of Loschmidt echo and quantum speed limit time for dynamical quantum phase transition in finite size systems. Our results illustrate that exact zeros of Loschmidt echo exist even in finite size quantum systems when the postquench parameter takes some discrete values in regions with the corresponding equilibrium phase different from the initial phase. As the system size increases and tends to infinity, the discrete parameters distribute continuously in the parameter regions. We further analyze the time for the appearance of the first exact zero of Loschmidt echo which is known as the quantum speed limit time $\tau_{\text{QSL}}$. We demonstrate that the maximal value of $\tau_{\text{QSL}}$ is proportional to $L$ and approaches infinity in the thermodynamical limit, when we quench the initial non-critical state to the critical phase. We also calculate the minimal value of $\tau_{\text{QSL}}$ and find that its behavior is dependent on the phase of initial state.