Field-Induced Ordered Phases in Anisotropic Spin-1/2 Kitaev Chains

TL;DR

This study investigates how magnetic fields induce various ordered phases in anisotropic spin-1/2 Kitaev chains, revealing complex field-dependent behaviors and novel phases through numerical and theoretical analysis.

Contribution

It introduces a detailed analysis of field-induced ordered phases in anisotropic Kitaev chains, employing DMRG and perturbation theory to uncover mechanisms behind these states.

Findings

Four-site and large unit-cell ordered phases appear when the field aligns with the strong bond.

A six-site periodicity phase with uniform chirality emerges at specific field angles.

Effective models reveal transverse Ising, Dzyaloshinskii-Moriya, and further-neighbor interactions.

Abstract

Motivated by intense research on two-dimensional spin-1/2 Kitaev materials, Kitaev spin chains and ladders, though geometrically limited, have been studied for their numerical simplicity and insights into extended Kitaev models. The phase diagrams under the magnetic field were also explored for these quasi-one dimensional models. For an isotropic Kitaev chain, it was found that a magnetic field polarizes the ground state except along the symmetric field angle, where the chain is found to remain gapless up to a critical field strength where it enters an intriguing soliton phase before reaching the polarized state at higher field strengths. Here we study an anisotropic Kitaev chain under a magnetic field using the density matrix renormalization group technique, where the ground state has a macroscopic degeneracy with a finite gap in the absence of the magnetic field. When the field is mainly aligned parallel to the strong bond, four-site and large unit-cell ordered phases arise. In a certain angle of the field, another ordered phase characterized by a uniform chirality with six-site periodicity emerges. We employ a perturbation theory to understand such field-induced ordered phases. The effective model uncovers the presence of transverse Ising and Dzyaloshinskii-Moriya interactions between unit cells, as well as further-neighbor Ising interaction induced by the magnetic field, which collectively explain the mechanisms behind these ordered states. Open questions and challenges are also discussed.