Topological entanglement entropy to identify topological order in quantum skyrmions

TL;DR

This paper demonstrates that topological entanglement entropy effectively distinguishes quantum skyrmion phases from helical phases in a 2D lattice, serving as a marker for quantum phase transitions.

Contribution

It introduces the use of topological entanglement entropy to identify and differentiate topologically ordered quantum skyrmion phases from other magnetic phases.

Findings

Topological entanglement entropy remains constant in the quantum skyrmion phase.

It exhibits fluctuations in the helical phase.

Topological entanglement entropy signals the quantum phase transition.

Abstract

We study the topological entanglement entropy and scalar chirality of a topologically ordered skyrmion formed in a two-dimensional triangular lattice. Scalar chirality remains a smooth function of the magnetic field in both helical and quantum skyrmion phases. In contrast, topological entanglement entropy remains almost constant in the quantum skyrmion phase, whereas it experiences enhanced fluctuations in the helical phase. Therefore, topological entanglement entropy is an effective tool to distinguish between the two phases and pinpoint the quantum phase transition in the system.