Quantum instability and edge entanglement in a quasi-long-range order

TL;DR

This paper explores how quantum systems with quasi-long-range order exhibit entanglement and topological features as external parameters change, highlighting the role of edge states and level crossings in finite systems.

Contribution

It introduces a detailed analysis of edge entanglement and topological order in the XX chain with a transverse field, emphasizing the finite-size effects and transition to the thermodynamic limit.

Findings

Multiple entanglement jumps occur at level crossings.

Edge spin entanglement signals topological order.

Kink-antikink pairs characterize the topological phase.

Abstract

We investigate the build-up of quasi-long-range order in the XX chain with transverse magnetic field at finite size. As the field is varied, the ground state of the system displays multiple level crossings producing a sequence of entanglement jumps. Using the partial fidelity and susceptibility, we study the transition to the thermodynamic limit and argue that the topological order can be described in terms of kink-antikink pairs and marked by edge spin entanglement.