Topological phase transitions in random Kitaev $\alpha$-chains

TL;DR

This paper investigates topological phase transitions in disordered Kitaev $lpha$-chains, revealing how disorder influences the phase diagram and the emergence of intermediate phases through analytical calculations of Lyapunov exponents.

Contribution

It provides an analytical study of Lyapunov exponents in a solvable disordered Kitaev chain model, elucidating the effects of disorder on topological phase transitions.

Findings

Disorder induces an intermediate phase between topological phases.

Direct transition between phases n=0 and n=2 occurs only without disorder.

Analytical calculation of Lyapunov exponents for Cauchy disorder.

Abstract

The topological phases of random Kitaev $\alpha$-chains are labelled by the number of localized edge Majorana Zero Modes. The critical lines between these phases thus correspond to delocalization transitions for these localized edge Majorana Zero Modes. For the random Kitaev chain with next-nearest couplings, where there are three possible topological phases $n=0,1,2$, the two Lyapunov exponents of Majorana Zero Modes are computed for a specific solvable case of Cauchy disorder, in order to analyze how the phase diagram evolves as a function of the disorder strength. In particular, the direct phase transition between the phases $n=0$ and $n=2$ is possible only in the absence of disorder, while the presence of disorder always induces an intermediate phase $n=1$, as found previously via numerics for other distributions of disorder.