Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram

Abstract

Fractional quantum Hall (FQH) system at Landau level filling fraction $\nu =5/2$ has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance ${\sigma }_{xy}=5e^2/2h$. Thermal Hall conductances of the Pf and APf states are quantized at ${\kappa }_{xy}=7/2$ and ${\kappa }_{xy}=3/2$ respectively in a proper unit. However, a recent experiment shows the thermal Hall conductance of $\nu =5/2$ FQH state is ${\kappa }_{xy}=5/2$. It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a ${\kappa }_{xy}=5/2$ phase. In this work, we do perturbative and non-perturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold ${\Lambda }_1$, which is lowered to an emergent U(1)$\times$U(1) symmetry at energy scales between ${\Lambda }_1$ and a higher value ${\Lambda }_2$, and is finally lowered to the composite fermion parity symmetry ${\mathbb{Z}}_2^F$ above ${\Lambda }_2$. Based on the emergent symmetries, we propose a phase diagram of the disordered $\nu =5/2$ FQH system, and show that a ${\kappa }_{xy}=5/2$ phase arises at disorder energy scales $\Lambda >{\Lambda }_1$. Furthermore, we show the gapped double-semion sector of $N_D$ compact domain walls contributes non-local topological degeneracy $2^{N_D-1}$, causing a low-temperature peak in the heat capacity. We implement a non-perturbative method to bootstrap generic topological 1+1D domain walls (2-surface defects) applicable to any 2+1D non-Abelian topological order. We identify potentially relevant spin TQFTs for various $\nu =5/2$ FQH states in terms of fermionic version of U(1)${}_{\pm 8}$ Chern-Simons theory $\times {\mathbb{Z}}_8$-class TQFTs.

44 pages, 9 figures, 3 tables. v2: Clarification/Refs added

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Cited by in corpus (55)

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• Isolated Ballistic Non-Abelian Interface Channel
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• Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
• Comment on S. H. Simon, Interpretation of thermal conductance of the $\nu =5/2$ edge, arXiv:1801.09687
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Partial equilibration of anti-Pfaffian edge modes at $\nu =5/2$
• Energetics of Pfaffian-AntiPfaffian Domains
• Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• Temperature enhancement of thermal Hall conductance quantization
• Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Quantum Hall hierarchy from coupled wires
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Energy relaxation in edge modes in the quantum Hall effect
• The chiral SYK model
• Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect
• Disorder-driven transition and intermediate phase for $\nu =5/2$ fractional quantum Hall effect
• Multiple Chiral Majorana Fermion Modes and Quantum Transport
• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Hong-Ou-Mandel heat noise in the quantum Hall regime
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$
• Non-Liquid Cellular States
• Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids
• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• An Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Emergent QCD${}_3$ Quantum Phase Transitions of Fractional Chern Insulators
• PH-Pfaffian order in a translationally and rotationally invariant system
• Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field
• Model interactions for Pfaffian paired states based on Chern-Simons field theory description
• Approximate two-body generating Hamiltonian for the PH-Pfaffian wavefunction
• Distribution of Conductances in Chiral Topological Superconductor Junctions
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Disorder broadening of even denominator fractional quantum Hall states in the presence of a short-range alloy potential
• Dynamics of Quantum Hall Interfaces
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Energy minimization of paired composite fermion wave functions in the spherical geometry
• Mean field approximations for short range four body interactions at $\nu =3/5$
• Integrability of the $\nu =4/3$ fractional quantum Hall edge states
• Phase transitions and topological properties of the 5/2 quantum Hall states with strong Landau-level mixing
• Edge Induced Topological Phase Transition of the Quantum Hall state at Half Filling
• Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State
• Composite fermion mass enhancement and particle-hole symmetry of fractional quantum Hall states in the lowest Landau level under realistic conditions
• The Second Landau Level Projection of Antiholomorphic Pfaffian Wavefunctions
• Quantized Transport of $\nu =2/3$ Fractional Quantum Hall Edge with Disordered Superconducting Proximity
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids