Left-left-right-right magnetic order in spin-1/2 Kitaev-Heisenberg chain

TL;DR

This paper investigates the phase diagram of the spin-1/2 Kitaev-Heisenberg chain, revealing a novel left-left-right-right magnetic order, analyzing its origin, and connecting it to 2D stripy order through quasi-1D insights.

Contribution

It identifies and explains a new magnetic phase in the Kitaev-Heisenberg chain and extends the understanding of its relation to 2D order using analytical and numerical methods.

Findings

Discovery of left-left-right-right magnetic order in the chain

Clarification of the order's origin via Luttinger liquid analysis

Demonstration of the phase's persistence with Gamma interaction

Abstract

In this work, we perform a combination of analytical and numerical studies on the phase diagram of the spin-1/2 Kitaev-Heisenberg chain in the region of negative Kitaev and positive Heisenberg couplings. Apart from the antiferromagnetic phase, we find a magnetically ordered phase with left-left-right-right order and a gapless phase with central charge value $c=1$, resolving the existing contradictory results in literature regarding this parameter region. In particular, the origin of the left-left-right-right order is clarified based on a perturbative Luttinger liquid analysis. The left-left-right-right phase is further shown to persist in the Kitaev-Heisenberg-Gamma model when a small nonzero Gamma interaction is introduced. Using a coupled-chain method, we also demonstrate that the one-dimensional (1D) left-left-right-right order gives a quasi-1D explanation for the 2D stripy order of the same model on the honeycomb lattice.