An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$

Abstract

We propose an effective field theory (EFT) of fractional quantum Hall systems near the filling fraction $\nu =5/2$ that flows to pertinent IR candidate phases, including non-abelian Pfaffian, anti-Pfaffian, and particle-hole Pfaffian states (Pf, APf, and PHPf). Our EFT has a 2+1$d$ O(2)${}_{2,L}$ Chern-Simons gauge theory coupled to four Majorana fermions by a discrete charge conjugation gauge field, with Gross-Neveu-Yukawa-Higgs terms. Including deformations via a Higgs condensate and fermion mass terms, we can map out a phase diagram with tunable parameters, reproducing the prediction of the recently-proposed percolation picture and its gapless topological quantum phase transitions. Our EFT captures known features of both gapless and gapped sectors of time-reversal-breaking domain walls between Pf and APf phases. Moreover, we find that Pf$\mid$APf domain walls have higher tension than domain walls in the PHPf phase. Then the former, if formed, may transition to the energetically-favored PHPf domain walls; this could, in turn, help further induce a bulk transition to PHPf.

arXiv comment72 pages, 10 figures, 5 tables. Many appendices. Add Sec 2.2, new remarks in Conclusion, and other clarifications. Accepted by Physical Review Research

References in corpus (55)

• Anyons in an exactly solved model and beyond
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Generalized Global Symmetries
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Observation of half-integer thermal Hall conductance
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Is the Composite Fermion a Dirac Particle?
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Condensate induced transitions between topologically ordered phases
• Quantized Thermal Transport in the Fractional Quantum Hall Effect
• Level/rank Duality and Chern-Simons-Matter Theories
• On 2-Group Global Symmetries and Their Anomalies
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Time-Reversal Breaking in QCD${}_4$, Walls, and Dualities in 2+1 Dimensions
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Topological boundary conditions, the BPS bound, and elimination of ambiguities in the quantum mass of solitons
• The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
• Particle-hole symmetry without particle-hole symmetry in the quantum Hall effect at ν = 5/2
• Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
• Dual Boundary Conditions in 3d SCFT's
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• Parton construction of a wave function in the anti-Pfaffian phase
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
• Time-Reversal Symmetry, Anomalies, and Dualities in (2+1)$d$
• On the Interpretation of Thermal Conductance of the nu=5/2 Edge
• On time-reversal anomaly of 2+1d topological phases
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Particle-Hole Symmetry Breaking and the 5/2 Fractional Quantum Hall Effect
• Anomaly indicators for time-reversal symmetric topological orders
• Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
• Finite Quantum Fluctuations About Static Field Configurations
• Effective mass and tricritical point for lattice fermions localized by a random mass
• Non-Abelian states with negative flux: a new series of quantum Hall states
• Comment on S. H. Simon, Interpretation of thermal conductance of the $\nu =5/2$ edge, arXiv:1801.09687
• Unambiguous one-loop quantum energies of 1+1 dimensional bosonic field configurations
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
• One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization
• Partial Equilibration of the Anti-Pfaffian edge due to Majorana Disorder
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Fermionic One-Loop Corrections to Soliton Energies in 1+1 Dimensions
• Energetics of Pfaffian-AntiPfaffian Domains
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• One-Loop Quantum Energy Densities of Domain Wall Field Configurations
• Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms
• Emergent QCD${}_3$ Quantum Phase Transitions of Fractional Chern Insulators

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• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
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• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Gauging Lie group symmetry in (2+1)d topological phases
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Phase transitions and topological properties of the 5/2 quantum Hall states with strong Landau-level mixing