Magnetic phase diagram of a spin-1/2 XXZ chain with modulated Dzyaloshinskii-Moriya interaction

TL;DR

This paper explores the complex ground-state phase diagram of a spin-1/2 XXZ chain with modulated Dzyaloshinskii-Moriya interaction under an alternating magnetic field, revealing multiple gapped and gapless phases and phase transitions.

Contribution

It introduces a detailed analysis of the phase diagram including new composite phases and their transitions using bosonization and numerical methods.

Findings

Identification of four distinct phases including two gapped and two gapless phases.

Discovery of quantum phase transitions driven by magnetic field variations.

Determination of the critical magnetic field for full polarization.

Abstract

We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with spatially modulated Dzyaloshinskii-Moriya interaction in the presence of applied along with the $\hat{z}$ axis alternating magnetic field. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of the magnetic field, the ground-state phase diagram of the model includes besides the ferromagnetic and gapless Luttiger-Liquid (LL) phases two gapped phases, the composite (C1) phase characterized by the coexistence of the long-range-ordered (LRO) alternating dimerization and the spin chirality patterns, and the composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. In the case of two-letter gapped phases, in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions (QPT) from a gapful phase into the gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalizations studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of the staggered component of the magnetic field vapes out the composite (C1) in favour of the composite gapped (C2) phase.