Distinguishing dynamical quantum criticality through local fidelity distances

TL;DR

This paper introduces local fidelity distances as a new tool to identify dynamical quantum phase transitions in one-dimensional Ising chains, offering a localized and potentially more practical alternative to the Loschmidt echo.

Contribution

It proposes a local quantum fidelity distance measure that detects critical times and exponents in dynamical quantum phase transitions, applicable to both integrable and non-integrable models.

Findings

Local fidelity distances identify non-analyticities at critical times.

The measure captures differences in eigenvalue distributions of subsystem density matrices.

Proposed distance measure works for models with oscillatory entanglement growth.

Abstract

Using local quantum fidelity distances, we study the dynamical quantum phase transition in integrable and non-integrable one-dimensional Ising chains. Unlike the Loschmidt echo, the standard measure for distinguishing between two quantum states to describe the dynamical quantum phase transition, the local fidelity requires only a part of the system to characterize it. The non-analyticities in the quantum distance between two subsystem density matrices identify the critical time and the corresponding critical exponent reasonably well in a finite-size system. Moreover, we propose a distance measure from the upper bound of the local quantum fidelity for certain quench protocols where the entanglement entropy features oscillatory growth in time. This local distance encodes the difference between the eigenvalue distribution of the initial and quenched subsystem density matrices and quantifies the critical properties. The alternative distance measure could be employed to examine the dynamical quantum phase transitions in a broader range of models, with implications for gaining insights into the transition from the entanglement perspective.