Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond

Abstract

The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian fractional quantum Hall (FQH) states at filling $\nu =k/(k+2)$. Computationally, the wave functions of these states are prohibitively expensive to generate for large systems. We introduce a series of parton states, denoted "${\bar{2}}^k{1}^{k+1}$," and show that they lie in the same universality classes as the particle-hole-conjugate RR ("anti-RR") states. Our analytical results imply that a $(U(1{)}_{k+1}\times U(2k{)}_{-1})/(SU(k{)}_{-2}\times U(1{)}_{-1})$ coset conformal field theory describes the edge excitations of the ${\bar{2}}^k{1}^{k+1}$ state, suggesting non-trivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequence "$\bar{n}{\bar{2}}^2{1}^4$," with $n=1,2,3$, to describe the FQH states observed at $\nu =2+1/2,2+2/5$ and $2+3/8$.

arXiv comment15 pages, 2 figures, includes supplemental material (published version)

References in corpus (57)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• 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
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Observation of the Fractional Quantum Hall Effect in Graphene
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Fractional Quantum Hall States and Jack Polynomials
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Entanglement entropy in fermionic Laughlin states
• Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
• Fractional Quantum Hall Effect of Composite Fermions
• Nonconventional odd denominator fractional quantum Hall states in the second Landau level
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Parafermion Hall states from coset projections of abelian conformal theories
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Exact Matrix Product States for Quantum Hall Wave Functions
• Fractional Quantum Hall Effect in the Second Landau Level
• Fractional Quantum Hall Phase Transitions and Four-flux Composite Fermions in Graphene
• Projective Construction of Non-Abelian Quantum Hall Liquids
• Composite Fermions and Broken Symmetries in Graphene
• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• High quality magnetotransport in graphene using the edge-free Corbino geometry
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Fibonacci anyons and charge density order in the 12/5 and 13/5 plateaus
• 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
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Observation of a Fractional Quantum Hall State at $\nu =1/4$ in a Wide GaAs Quantum Well
• Spinful Composite Fermions in a Negative Effective Field
• Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment
• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level
• Fractional Quantum Hall Effect at Landau Level Filling nu=4/11
• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Role of exciton screening in the 7/3 fractional quantum Hall effect
• Observation of fractional quantum Hall effect at even-denominator 1/2 and 1/4 fillings in asymmetric wide quantum wells
• Effective Field Theory and Projective Construction for the Z_k Parafermion Fractional Quantum Hall States
• Observation of Incompressibility at $\nu =4/11$ and $\nu =5/13$
• Non-Abelian states with negative flux: a new series of quantum Hall states
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Phase Diagrams for the $\nu$ = 1/2 Fractional Quantum Hall Effect in Electron Systems Confined to Symmetric, Wide GaAs Quantum Wells
• Transition from Abelian to non-Abelian quantum liquids in the second Landau level
• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Quantum Hall States at $\nu =\frac{2}{k+2}$
• Geometric construction of Quantum Hall clustering Hamiltonians
• The enigmatic 12/5 fractional quantum Hall effect
• The enigma of the $\nu =2+\frac{3}{8}$ fractional quantum Hall effect
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Constructing topological models by symmetrization: A PEPS study
• States of interacting composite fermions at Landau level fillig $\nu =2+3/8$

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• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Abelian topological order of $\nu =2/5$ and $3/7$ fractional quantum Hall states in lattice models
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Local density of states and particle entanglement in topological quantum fluids
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Dynamical topological excitations in parafermion chains
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Fractional Quantum Hall States of the $\mathcal{A}$ phase in the Second Landau Level
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• A composite particle construction of the Fibonacci fractional quantum Hall state
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Non-Abelian phases from the condensation of Abelian anyons
• Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State
• Fractionally Quantized Electric Polarization and Discrete Shift of Crystalline Fractional Chern Insulators
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures
• Composite fermions and parton wavefunctions in twisted graphene on hexagonal boron nitride
• Crossover from Integer to Fractional Quantum Hall Effect