Superuniversality from disorder at two-dimensional topological phase transitions

TL;DR

This paper demonstrates that certain two-dimensional topological phase transitions under disorder exhibit superuniversal critical behavior, governed by the same infinite-randomness fixed point as the 2D random transverse-field Ising model, validated through simulations.

Contribution

It reveals superuniversal critical scaling in disordered 2D topological transitions, linking them to the infinite-randomness fixed point of the 2D random transverse-field Ising model.

Findings

Critical behavior is superuniversal across various topological transitions.

Critical exponents match those of the 2D random transverse-field Ising model.

Large-scale quantum Monte Carlo confirms the theoretical predictions.

Abstract

We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles (`anyons') identified with `electric charge' excitations of a phase with intrinsic topological order. All other anyons have nontrivial mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is `superuniversal' across a wide range of such condensation transitions, and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases.