Topological phase transitions between bosonic and fermionic quantum Hall states near even-denominator filling factors

TL;DR

This paper investigates the quantum critical point between fermionic and bosonic quantum Hall states near even-denominator filling factors, revealing a cascade of topological phase transitions involving neutral Dirac fermions and intermediate topologically ordered phases.

Contribution

It introduces a novel partonic framework to describe the transition, connecting it to an invertible $E_8$ state and multiple intermediate phases, advancing understanding of topological phase transitions.

Findings

Transition described as cascade of mass changes in neutral Dirac fermions

Presence of at least three intermediate topologically ordered phases

Transition involves a shift from an invertible $E_8$ state to trivial topology

Abstract

We study the quantum critical point between the fermionic $\nu=8$ quantum Hall state and the bosonic $\nu=2$ quantum Hall state of Cooper pairs. Our study is motivated by the composite fermion construction for the daughter states of even-denominator fractional quantum Hall states and the experimentally observed transition between the daughter and the Jain states at the same filling. We show that this transition is equivalent to the transition between a neutral invertible $E_8$ state and a topologically trivial state. These transitions can be described in a partonic framework as a cascade of mass changes of four neutral Dirac fermions coupled to multiple Abelian Chern-Simons $U(1)$ gauge fields. In the absence of fine-tuning, the transition is split into a series of four or more different transitions, with at least three distinct intermediate topologically ordered phases hosting neutral anyons.