Topological Phase Transition under Infinite Randomness

TL;DR

This paper explores how strong disorder affects topological phase transitions in fermionic chains, revealing gapless phases and infinite randomness critical points driven by fluctuation scales.

Contribution

It introduces a novel analysis of topological phase transitions under strong disorder, highlighting the role of fluctuation scales and infinite randomness fixed points.

Findings

Both trivial and topological phases become gapless with Griffiths-like regions.

The phase transition is governed by fluctuation scales, not the mean.

Critical behavior is characterized by an infinite randomness fixed point with an irrational central charge.

Abstract

In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated criticality can fundamentally change. Here we investigate topological properties of a strongly disordered fermionic chain where the bond couplings are drawn from normal probability distributions which are defined by characteristic standard deviations. Using numerical strong disorder renormalization group methods along with analytical techniques, we show that the competition between fluctuation scales renders both the trivial and topological phases gapless with Griffiths like rare regions. Moreover, the transition between these phases is solely governed by the fluctuation scales, rather than the means, rendering the critical behavior to be determined by an infinite randomness fixed point with an irrational central charge. Our work points to a host of novel topological phases and atypical topological phase transitions which can be realized in systems under strong disorder.