Antiferromagnetic magnons from fractionalized excitations

TL;DR

This paper introduces a novel fermionic approach using Chern-Simons theory to describe antiferromagnetic magnons, linking fractionalized excitations to conventional magnon behavior in Ne9el states.

Contribution

It develops a Chern-Simons fermion framework that captures magnon excitations and explores effects of frustration and anyonic statistics in quantum spin systems.

Findings

High-precision agreement between CS magnons and traditional Ne9el magnons

Identification of long-range multi-leg interactions due to frustration

Application of theory to tunable anyon models

Abstract

We develop an approach to describe antiferromagnetic magnons on a bipartite lattice supporting the N\'{e}el state using fractionalized degrees of freedom typically inherent to quantum spin liquids. In particular we consider a long-range magnetically ordered state of interacting two-dimensional quantum spin$-1/2$ models using the Chern-Simons (CS) fermion representation of interacting spins. The interaction leads to Cooper instability and pairing of CS fermions, and to CS superconductivity which spontaneously violates the continuous $\mathrm{U}(1)$ symmetry generating a linearly-dispersing gapless Nambu-Goldstone mode due to phase fluctuations. We evaluate this mode and show that it is in high-precision agreement with magnons of the corresponding N\'{e}el antiferromagnet irrespective to the lattice symmetry. Using the fermion formulation of a system with competing interactions, we show that the frustration gives raise to nontrivial long-range four, six, and higher-leg interaction vertices mediated by the CS gauge field, which are responsible for restoring of the continuous symmetry at sufficiently strong frustration. We identify these new interaction vertices and discuss their implications to unconventional phase transitions. We also apply the proposed theory to a model of anyons that can be tuned continuously from fermions to bosons.