Binary disorder in quantum Ising chains and induced Majorana zero modes

TL;DR

This paper investigates how binary disorder in 1D quantum Ising chains induces Majorana zero modes, revealing their boundary localization, fractal size distribution, and connection to spin glass transitions.

Contribution

It demonstrates the emergence of Majorana zero modes due to binary disorder in extended quantum Ising models, linking disorder configurations to topological boundary states.

Findings

Zero energy Majorana modes appear when disorder spans different winding numbers.

Majorana pairs exhibit fractal size distribution at critical points.

Longer ranged interactions lead to a spin glass transition.

Abstract

Dynamical structure factor (S(k,$\omega$)) is calculated for the one-dimensional (1D) transverse field Ising model, and its recent extension to include a three spin term, with quenched binary disorder. We study the low energy modes for lattices as large as 256 sites. We show that the intense zero energy modes appear whenever the binary disorder straddles two different winding numbers. We argue that these are Majorana modes, which reside on the boundaries of the rare regions. The size distribution of Majorana pairs has a fractal behavior at the critical points. With the longer ranged interactions a spin glass transition is observed as well.