Phase Diagram and Entanglement of Ising Model With Dzyaloshinskii-Moriya Interaction

TL;DR

This paper investigates the phase diagram and entanglement properties of a one-dimensional Ising model with Dzyaloshinskii-Moriya interaction, revealing critical points, phase transitions, and the role of entanglement in the system.

Contribution

The study applies quantum renormalization group and exact diagonalization to characterize phases, order parameters, and entanglement scaling in the Ising model with DM interaction, highlighting new chiral order insights.

Findings

Identification of antiferromagnetic and chiral phases.

Critical point determined by divergence of structure factor.

Entanglement exhibits nonanalytic behavior at phase transitions.

Abstract

We have studied the phase diagram and entanglement of the one dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has two phases, antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of new spin operators which are defined by a nonlocal transformation.