Interplay between the Dzyaloshinskii-Moriya term and external fields on spin transport in the spin-1/2 one-dimensional antiferromagnet

Highlights: • The quantum phase diagram is studied using abelian bosonization. • The spin conductivity is calculated using bosonization abelian and the Kubo formalism. • The influence of the quantum phase transition on AC spin conductivity is analyzed. We study the effect of the uniform Dzyaloshinskii-Moriya interaction (symmetric exchange anisotropy) and arbitrary oriented external magnetic fields on spin conductivity in the spin-1/2 one-dimensional Heisenberg antiferromagnet. The spin conductivity is calculated employing abelian bosonization and the Kubo formalism of transport. We investigate the influence of three competing phases at zero-temperature, (Néel phase, dimerized phase and gapless Luttinger liquid phase) on the AC spin conductivity.