Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions

Abstract

The Moore-Read Pfaffian (Pf) state exhibits two distinct neutral excitation modes, the bosonic magnetoroton mode, and the neutral fermion mode. These two modes have been conjectured to be supersymmetric (SUSY) partners in the long-wavelength limit. Previous studies on these neutral excitations of the Pf state have shown evidence in favor of SUSY in the vicinity of the second Landau level (SLL) Coulomb interaction. Inspired by that, using the framework of parton theory, we test the SUSY conjecture for a state that lies in the same universality class as the particle-hole conjugate of the Pf, namely the anti-Pf (aPf) state, by constructing explicit wave functions for its magnetoroton and neutral fermion excitations and evaluating them for very large system sizes. As with the previous studies on the Pf state, we find that the long-wavelength gaps of the neutral modes of the parton state belonging to the same topological class as the aPf are close to each other for the SLL Coulomb interaction. Furthermore, using the parton wave functions, we compute the dispersion of various neutral collective excitations, including the magnetoroton, neutral fermion, and parton-excitons, for several notable non-Abelian and Abelian states. Finally, we propose a parton-exciton ansatz for the gapped neutral excitation of the composite fermion Fermi liquid at quarter filling and compute its dispersion for the Coulomb interaction in the lowest Landau level.

References in corpus (114)

• 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
• "Deconfined" quantum critical points
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Fractional statistics in anyon collisions
• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• 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
• Liquid Crystal Phases of Quantum Hall Systems
• Geometrical Description of the Fractional Quantum Hall Effect
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Robust fractional quantum Hall states and continuous quantum phase transitions in a half-filled bilayer graphene Landau level
• Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
• Quantum Hall fractions in rotating Bose-Einstein condensates
• 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
• Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• Band Structure of the Fractional Quantum Hall Effect
• Excitation gaps in fractional quantum Hall states: An exact diagonalization study
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Fractional Quantum Hall Effect in the Second Landau Level
• Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect
• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Fibonacci anyons and charge density order in the 12/5 and 13/5 plateaus
• Field theory of the quantum Hall nematic transition
• Parton construction of a wave function in the anti-Pfaffian phase
• Imaging tunable quantum Hall broken-symmetry orders in graphene
• Quantum Hall fractions for spinless Bosons
• Magneto-roton excitation of fractional quantum Hall effect: Comparison between theory and experiment
• Chiral Gravitons in Fractional Quantum Hall Liquids
• Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene
• Observation of a Fractional Quantum Hall State at $\nu =1/4$ in a Wide GaAs Quantum Well
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Theory of Nematic Fractional Quantum Hall State
• Spinful Composite Fermions in a Negative Effective Field
• Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment
• Generalized Quantum Hall Projection Hamiltonians
• Composite Fermions in Negative Effective Magnetic Field: A Monte-Carlo Study
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
• Fractional Quantum Hall Effect at Landau Level Filling nu=4/11
• Fractional statistics in the fractional quantum Hall effect
• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons
• Observation of fractional quantum Hall effect at even-denominator 1/2 and 1/4 fillings in asymmetric wide quantum wells
• Composite fermion theory of collective excitations in fractional quantum Hall effect
• Numerical study of charge and statistics of Laughlin quasi-particles
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Observation of Incompressibility at $\nu =4/11$ and $\nu =5/13$
• 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
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• Charge and Statistics of Quantum Hall Quasi-Particles. A numerical study of mean values and fluctuations
• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• Competing Topological Orders in the nu=12/5 Quantum Hall State
• Unpaired composite fermion, topological exciton, and zero mode
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Quantum Hall States at $\nu =\frac{2}{k+2}$
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• Excitons of Composite Fermions
• The enigmatic 12/5 fractional quantum Hall effect
• Berry phases for composite fermions: effective magnetic field and fractional statistics
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene
• Interplay between fractional quantum Hall liquid and crystal phases at low filling
• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• Positions of the magnetoroton minima in the fractional quantum Hall effect
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Microscopic Model for Fractional Quantum Hall Nematics
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Composite fermion pairing induced by Landau level mixing
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Topological phase transition between composite-fermion and Pfaffian daughter states near ν = 1/2 FQHS
• Collective excitations at filling factor 5/2: The view from superspace
• Dirac Composite Fermion Theory of General Jain's Sequences
• 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
• STM in the fractional quantum Hall effect: Spectroscopy of composite-fermion bound states
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions
• Composite fermion Hall conductivity and the half-filled Landau level
• Local density of states and particle entanglement in topological quantum fluids
• Supergravity model of the Haldane-Rezayi fractional quantum Hall state
• Fingerprints of Composite Fermion Lambda Levels in Scanning Tunneling Microscopy
• Signatures of Supersymmetry in the $\nu =5/2$ Fractional Quantum Hall Effect
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Single-particle spectral function of fractional quantum anomalous Hall states
• Developing fractional quantum Hall states at even-denominator fillings 1/6 and 1/8
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• 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
• Composite fermions in a wide quantum well in the vicinity of the filling factor 1/2
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells

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