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

2025/08/24 by Zheltonozhskii, Evgenii, Stern, Ady, Lindner, Netanel H.
#FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2508.17457

Abstract

We study the quantum critical point between the fermionic ν=8 quantum Hall state and the bosonic ν=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 E₈ 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.

Citations

• Fractional quantum Hall state at ν= 1/2 with energy gap up to 6 K, and possible transition from one- to two-component state
• The numerical case for identifying paired quantum Hall phases by their daughters
• Majorana edge reconstruction and the ν=5/2 non-Abelian thermal Hall puzzle
• Ordering the topological order in the fractional quantum Hall effect
• Paired Parton Trial States for the Superfluid-Fractional Chern Insulator Transition
• Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of ABA Trilayer Graphene
• Fractionalization as an alternate to charge ordering in electronic insulators
• Hierarchy construction for non-abelian fractional quantum Hall states via anyon condensation
• Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene
• High-Resolution Tunneling Spectroscopy of Fractional Quantum Hall States
• Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene
• Quantum Hall physics: Hierarchies and conformal field theory techniques
• Short-range entanglement and invertible field theories
• Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions
• Bosonic Topological Insulators and Paramagnets: a view from cobordisms
• Non-Abelian anyons and topological quantum computation
• Anyons in an exactly solved model and beyond
• Classification of abelian spin Chern-Simons theories
• Nonabelions in the fractional quantum hall effect

Related

• Symmetry protected bosonic topological phase transitions: Quantum Anomalous Hall system of weakly interacting spinor bosons in a square lattice
• Bosonic Halperin fractional quantum Hall effect at filling factor ν=2/5
• Alteration of Topology in Quantum Phase Transitions via Symmetry Enrichment
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Continuous transition and gapless roton inside fractional quantum anomalous Hall states