Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

TL;DR

This study combines analytical and numerical methods to explore the phase diagram of a Heisenberg chain with Dzyaloshinskii-Moriya interaction and magnetic field, revealing Ising ordered phases and a Luttinger liquid state.

Contribution

It provides the first comprehensive phase diagram of the model, confirming theoretical predictions and identifying dominant N z Néel Ising order under certain conditions.

Findings

Identification of two Ising ordered phases

Confirmation of a critical Luttinger liquid phase

Prevalence of N z Néel Ising order in specific regimes

Abstract

We report a combined analytical and density matrix renormalized group study of the antiferromagnetic XXZ spin-1/2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic field. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [Phys. Rev. B 81, 144419 (2010)]. We also confirm the prevalence of the N z N\'eel Ising order in the regime of comparable DM and magnetic field magnitudes.