Topological phases of a Kitaev tie

TL;DR

This paper explores the topological phases of a novel Kitaev chain configuration called the Kitaev tie, analyzing how the knot position influences topological properties and phase stability.

Contribution

It introduces the concept of a Kitaev tie, a frustrated system with topological phases dependent on the knot position, expanding understanding of topological matter.

Findings

Topological phases depend on the knot position and chemical potential.

The phase diagram reveals regions of topological and trivial phases.

Topological frustration affects the stability of the system.

Abstract

We investigate the topological properties of a Kitaev chain in the shape of a legged-ring, which is here referred to as Kitaev tie. We demonstrate that the Kitaev tie is a frustrated system in which topological properties are determined by the position of the movable bond (the tie knot). We determine the phase diagram of the system as a function of the knot position and chemical potential, also discussing the effects of topological frustration. The stability of the topological Kitaev tie is addressed by a careful analysis of the system free energy.