Chiral Partition Functions of Quantum Hall Droplets

Abstract

Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finite-dimensional representation of the modular group. The partition functions are derived and used to describe electron transitions leading to Coulomb blockade conductance peaks. We find the peak patterns for Abelian hierarchical states and non-Abelian Read-Rezayi states, and compare them. Experimental observation of these features can check the qualitative properties of the conformal field theory description, such as the decomposition of the Hilbert space into sectors, involving charged and neutral parts, and the fusion rules.

37 pages, 8 figures

References in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons and the quantum Hall effect - a pedagogical review
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Fractional Quantum Hall Effect in the Second Landau Level
• The non-Abelian Interferometer
• Topological Entanglement Entropy from the Holographic Partition Function
• Coulomb blockade as a probe for non-Abelian statistics in Read-Rezayi states
• Relevance of multiple-quasiparticle tunneling between edge states at ν=p/(2np+1)
• Experimental signatures of non-Abelian statistics in clustered quantum Hall states
• Correlated tunneling and the instability of the fractional quantum Hall edge

Cited by in corpus (18)

• Protected edge modes without symmetry
• Quantum Hall Physics - hierarchies and CFT techniques
• Interacting topological phases and modular invariance
• Bulk-boundary correspondence in (3+1)-dimensional topological phases
• Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
• Bosonic topological phases of matter: bulk-boundary correspondence, SPT invariants and gauging
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Warped Weyl fermion partition functions
• Charge tunneling in fractional edge channels
• Interference, Coulomb blockade, and the identification of non-abelian quantum Hall states
• Charged Topological Entanglement Entropy
• Boundary theory of the X-cube model in the continuum
• Partition Functions of Non-Abelian Quantum Hall States
• Relative Anomaly in (1+1)d Rational Conformal Field Theory
• Thermal broadening of the Coulomb blockade peaks in quantum Hall interferometers
• Thermoelectric properties of Coulomb-blockaded fractional quantum Hall islands
• Thermopower and thermoelectric power factor of ${\mathbb{Z}}_k$ parafermion quantum dots
• Quasiparticle agglomerates in Read-Rezayi and anti Read-Rezayi state