# Criticality and factorization in the Heisenberg chain with Dzyaloshinskii-Moriya interaction

## TL;DR

This paper investigates the ground state properties and phase transitions of an anisotropic Heisenberg XYZ chain with Dzyaloshinskii-Moriya interaction, revealing criticality, phase diagram, and coherence-based indicators of quantum phase transitions.

## Contribution

It introduces the use of Wigner-Yanase skew information as a coherence witness for detecting quantum phase transitions in the model.

## Key findings

- WYSI effectively detects quantum phase transitions.
- Identification of a phase diagram with three distinct phases.
- Factorization volume in the chiral phase due to DM interactions.

## Abstract

In this work, we address the ground state properties of the anisotropic spin-1/2 Heisenberg XYZ chain under the interplay of magnetic fields and the Dzyaloshinskii-Moriya (DM) interaction which we interpret as an electric field. The identification of the regions of enhanced sensitivity determines criticality in this model. We calculate the Wigner-Yanase skew information (WYSI) as a coherence witness of an arbitrary two-qubit state under specific measurement bases. The WYSI is demonstrated to be a good indicator for detecting the quantum phase transitions. The finite-size scaling of coherence susceptibility is investigated. We find that the factorization line in the antiferromagnetic phase becomes the factorization volume in the gapless chiral phase induced by DM interactions, implied by the vanishing concurrence for a wide range of field. We also present the phase diagram of the model with three phases: antiferromagnetic, paramagnetic, and chiral, and point out a few common mistakes in deriving the correlation functions for the systems with broken reflection symmetry.