Mutual information and correlations across topological phase transitions in topologically ordered graphene zigzag nanoribbons

TL;DR

This study investigates how mutual information and correlations evolve during topological phase transitions in graphene zigzag nanoribbons, revealing persistent entanglement patterns and their weakening in crossover phases.

Contribution

It provides the first detailed analysis of mutual information across topological phase transitions in graphene nanoribbons, highlighting entanglement behavior changes.

Findings

Strong entanglement between A- and B-chirality carbon lines in topological phase

Entanglement persists but weakens in crossover phases

No long-range entanglement in symmetry-protected phase without disorder

Abstract

Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following results: (i) In the topologically ordered phase, A-chirality carbon lines strongly entangle with B-chirality carbon lines on the opposite side of the zigzag ribbon. This entanglement persists but weakens in crossover phases. (ii) The upper zigzag edge entangles with non-edge lines of different chirality on the opposite side of the ribbon. (iii) Entanglement increases as more carbon lines are grouped together, regardless of the lines' chirality. No long-range entanglement was found in the symmetry-protected phase in the absence of disorder.