Interplay between Symmetric Exchange Anisotropy, Uniform Dzyaloshinskii-Moriya Interaction and Magnetic Fields in the Phase Diagram of Quantum Magnets and Superconductors

TL;DR

This paper theoretically explores how symmetric exchange anisotropy, Dzyaloshinskii-Moriya interactions, and magnetic fields influence the phase diagram of one-dimensional quantum antiferromagnets, revealing three competing phases and their stability.

Contribution

It introduces a comprehensive analysis of the combined effects of DM interactions, exchange anisotropy, and magnetic fields on quantum spin chains, including phase stability and experimental analogues.

Findings

Identification of three main phases: antiferromagnet, dimerized antiferromagnet, and Luttinger liquid.

Small magnetic field component along the DM vector destroys certain phases.

Critical easy-plane anisotropy destabilizes phase (i) beyond a threshold.

Abstract

We theoretically study the joint influence of uniform Dzyaloshinskii-Moriya (DM) interactions, symmetric exchange anisotropy (with its axis parallel to the DM vector) and arbitrarily oriented magnetic fields on one-dimensional spin 1/2 antiferromagnets. We show that the zero-temperature phase diagram contains three competing phases: (i) an antiferromagnet with Neel vector in the plane spanned by the DM vector and the magnetic field, (ii) a {\em dimerized} antiferromagnet with Neel vector perpendicular to both the DM vector and the magnetic field, and (iii) a gapless Luttinger liquid. Phase (i) is destroyed by a small magnetic field component along the DM vector and is furthermore unstable beyond a critical value of easy-plane anisotropy, which we estimate using Abelian and non-Abelian bosonization along with perturbative renormalization group. We propose a mathematical equivalent of the spin model in a one-dimensional Josephson junction (JJ) array located in proximity to a bulk superconductor. We discuss the analogues of the magnetic phases in the superconducting context and comment on their experimental viability.