Nonperturbative emergence of Dirac fermion in strongly correlated composite fermions of fractional quantum Hall effects

Abstract

The classic composite fermion field theory (Ref. 1) builds up an excellent framework to uniformly study important physical objects and globally explain anomalous experimental phenomena in fractional quantum Hall physics while there are also inherent weaknesses. We present a nonperturbative emergent Dirac fermion theory from this strongly correlated composite fermion field theory, which overcomes these serious long-standing shortcomings. The particle-hole symmetry of Dirac equation resolves this particle-hole symmetry enigma in the composite fermion field theory. With the help of presented numerical data, we show that for main Jain's sequences of fractional quantum Hall effects, this emergent Dirac fermion theory is most likely nonperturbatively stable.

arXiv comment7 pages, 1 table, 1 figure, published version

References in corpus (37)

• Electric Field Effect in Atomically Thin Carbon Films
• Topological Insulators
• Topological insulators and superconductors
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Is the Composite Fermion a Dirac Particle?
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Dual Dirac liquid on the surface of the electron topological insulator
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Towards a field theory of the fractional quantum Hall states
• The half-filled Landau level: the case for Dirac composite fermions
• Excitation gaps in fractional quantum Hall states: An exact diagonalization study
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• Stability and effective masses of composite-fermions in the first and second Landau Level
• What Determines the Fermi Wave Vector of Composite Fermions?
• Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement
• Mirror symmetry and the half-filled Landau level
• Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
• Striped quantum Hall state in a half-filled Landau level
• Fractional Quantum Hall States at 1/3 and 5/2 Filling: the Density-Matrix Renormalization Group Calculations
• Thermoelectric transport signatures of Dirac composite fermions in the half-filled Landau level
• Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries
• The $\nu =\frac{1}{2}$ Landau level: Half-full or half-empty?
• Fermi Contour Anisotropy of GaAs Electron-Flux Composite Fermions in Parallel Magnetic Fields
• Hole-flux Composite Fermion Commensurability Oscillations
• The Dirac composite fermion of the fractional quantum Hall effect
• Effective Mass of Composite Fermions and Fermionic Chern-Simons Theory in Temporal Gauge
• Numerical Test of Disk Trial Wave function for Half-Filled Landau Level
• Correlation-hole induced paired quantum Hall states in lowest Landau level
• Interaction and dimensionality in the quantum Hall physics

Cited by in corpus (1)

• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect