Spin- and Flux-gap Renormalization in the Random Kitaev Spin Ladder

TL;DR

This paper investigates the effects of randomness on the Kitaev spin ladder, revealing how spin and flux gaps behave under strong disorder using real-space renormalization group analysis.

Contribution

It introduces a detailed analysis of the random Kitaev spin ladder, highlighting the distinct renormalization behaviors of spin and flux gaps in different coupling limits.

Findings

Spin gap behavior aligns with the random transverse-field Ising chain in the Ising limit.

Flux gap is mainly influenced by y-coupling, showing unique renormalization.

Z-couplings exhibit non-universal disorder criticality at low energies.

Abstract

We study the Kitaev spin ladder with random couplings by using the real-space renormalization group technique. This model is the minimum model in Kitaev systems that has conserved plaquette fluxes, and its quasi-one-dimensional geometry makes it possible to study the strong-disorder fixed points for both spin- and flux- excitation gaps. In the Ising limit, the behavior of the spin gap is consistent with the familiar random transverse-field Ising chain, but the flux gap is dominated by the y-coupling. In the XX limit, while the x- and y-couplings are renormalized simultaneously, the z-couplings are not renormalized drastically and lead to non-universal disorder criticality at low-energy scales.