Percolation Transition in a Topological Phase

TL;DR

This paper investigates how topological phases behave under geometric disorder introduced by bond percolation, revealing complex phenomena like fractured topological regions with many topological clusters.

Contribution

The study introduces and analyzes toy models of topological phases subjected to bond percolation, uncovering new crossover regimes and boundary phenomena due to geometrical disorder.

Findings

Identification of fractured topological regions with multiple topological clusters

Discovery of boundary phenomena influenced by competing energy scales

Rich phenomenology and crossover regimes in disordered topological systems

Abstract

Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an underlying topological phase. To understand this physics we introduce and study both short and long-ranged toy models where a one dimensional topological phase is subjected to bond percolation protocols. We find that non-trivial boundary phenomena follow competing energy scales even while global topological response is governed via geometrical properties of the percolated lattice. Using numerical, analytical and appropriate mean-field studies we uncover the rich phenomenology and the various cross-over regimes of these systems. In particular, we discuss emergence of "fractured topological region" where an overall trivial system contains macroscopic number of topological clusters. Our study shows the interesting physics that can arise from an interplay of geometrical disorder within a topological phase.