Quantum coherence and uncertainty in the anisotropic XY chain

TL;DR

This paper investigates how local quantum coherence and uncertainty, based on Wigner-Yanase skew information, can detect quantum phase transitions and ground state factorization in the anisotropic XY spin chain, highlighting their effectiveness and limitations.

Contribution

It demonstrates the utility of skew information in identifying phase transitions and ground state factorization, introduces an experimentally friendly lower bound, and discusses the limitations of non-analyticity as a universal indicator.

Findings

Skew information reveals second order phase transitions.

A simple lower bound effectively indicates quantum coherence.

Non-analyticities in local quantum uncertainty are not always linked to phase transitions.

Abstract

We explore the local quantum coherence and the local quantum uncertainty, based on Wigner-Yanase skew information, in the ground state of the anisotropic spin-1/2 XY chain in transverse magnetic field. We show that the skew information, as a figure of merit, supplies the necessary information to reveal the occurrence of the second order phase transition and the completely factorized ground state in the XY model. Additionally, in the same context, we also discuss the usefulness of a simple experimentally friendly lower bound of local quantum coherence. Furthermore, we demonstrate how the connection between the appearance of non-analyticities in the local quantum uncertainty of the ground state and the quantum phase transitions does not hold in general, by providing explicit examples of the situation. Lastly, we discuss the ability of the local quantum coherence to accurately estimate the critical point of the phase transition, and investigate the robustness of the factorization phenomenon at low temperatures.