Conditional global entanglement in a Kosterlitz-Thouless quantum phase transition

TL;DR

This paper investigates the effectiveness of conditional global entanglement as an indicator of Kosterlitz-Thouless quantum phase transitions, demonstrating its ability to detect transition points and characterize different phases.

Contribution

The study introduces conditional global entanglement as a novel and effective measure for identifying KT phase transitions and characterizing phases, overcoming limitations of traditional entanglement measures.

Findings

Conditional global entanglement peaks at the KT transition point.

Traditional global entanglement does not reliably indicate KT transitions.

Conditional global entanglement distinguishes different phases effectively.

Abstract

Entanglement is known as an important indicator for characterizing different types of quantum phase transitions (QPTs), however it faces some challenges in the Kosterlitz-Thouless (KT) phase transitions due to an essential singularity which cannot be identified in finite derivatives of the ground state energy. In this paper, we consider global entanglement (GE) in a KT phase transition and show that while it does not indicate any clear signature of the phase transition, the conditional version of GE is a good indicator with strong signatures of the KT transition. In particular, we study a deformed version of the $Z_d$ Kitaev model which has an intermediate KT phase which separates a $Z_d$ topological phase from a magnetized phase at two different KT transition points. Using a mapping to the classical $d$-state clock model, we consider GE and the generalized GE and show that they do not provide a reliable indicator of transition points. However, their difference called conditional global entanglement (Q) shows a peak at the first KT transition point. Additionally, we show that it can characterize various phases of the model as it behaves substantially different in each phase. We therefore conclude that Q is a useful measure that can characterize various phases of KT QPTs as well as their related critical points.