A Spin $1/2$ Fermions Chain with $XY$ Interaction

TL;DR

This paper studies a chain of spinful fermions with XY interaction, revealing a topological phase transition between trivial and non-trivial phases, characterized by a protected bosonic zero mode.

Contribution

It maps a spinful fermion chain with XY interaction onto a Kitaev chain and analyzes its topological phases and quantum phase transition.

Findings

Identification of a topological phase with a protected zero mode

Determination of the phase diagram via finite-size scaling

Observation of a quantum phase transition between phases

Abstract

We consider a chain of spinful fermions with nearest neighbor hopping in the presence of a $XY$ antiferromagnetic interaction. The $XY$ term is mapped onto a Kitaev chain at half-filling such that displays a bosonic zero mode topologically protected and long-range order. As the strength of the hopping amplitude is changed, the system undergoes a quantum phase transition from the topological non-trivial to the trivial phase. We apply the finite-size scaling method to determinate the phase diagram of the model.