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

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 [I. Garate and I. 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.