Topological spin ordering via Chern-Simons superconductivity

TL;DR

This paper introduces a novel topological magnetic state in 2D quantum spin models using Chern-Simons fermion representation, revealing a topologically non-trivial superconductor with coexisting magnetic order.

Contribution

It constructs a topological, long-range ordered state in 2D spin models via Chern-Simons fermion approach, identifying a new class of symmetry protected topological states.

Findings

Discovery of a topologically non-trivial CS superconductor in a honeycomb XY model

Demonstration of coexistence of magnetic order and topological properties

Identification of physical signatures of the topological state

Abstract

We use the Chern-Simons (CS) fermion representation of s =1/2 spin operators to construct topological, long-range magnetically ordered states of interacting two-dimensional (2D) quantum spin models. We show that the fermion-fermion interactions mediated by the dynamic CS flux attachment may give rise to Cooper pairing of the fermions. Specifically, in an XY model on the honeycomb lattice, this construction leads to a "CS superconductor," which belongs to a topologically non-trivial in 2D symmetry class DIII, with particle-hole and time-reversal symmetries. It is shown that in the original spin language, this state corresponds to a symmetry protected topological state, which coexists with a magnetic long-range order. We discuss physical manifestations of the topological character of the corresponding state and requirements for models that could host it.