Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect

Abstract

It is commonly assumed in the studies of the fractional quantum Hall effect that the physics of a fractional quantum Hall state, in particular the character of its excitations, is invariant under a continuous deformation of the Hamiltonian during which the gap does not close. We show in this article that, at least for finite systems, as the interaction is changed from a model three body interaction to Coulomb, the ground state at filling factor $\nu =2/5$ evolves continuously from the so-called Gaffnian wave function to the composite fermion wave function, but the quasiholes alter their character in a nonperturbative manner. This is attributed to the fact that the Coulomb interaction opens a gap in the Gaffnian quasihole sector, pushing many of the states to very high energies. Interestingly, the states below the gap are found to have a one-to-one correspondence with the composite fermion theory, suggesting that the Gaffnian model contains composite fermions, and that the Gaffnian quasiholes are unstable to the formation of composite fermions when a two-body interaction term is switched on. General implications of this study are discussed.

11 pages, 8 figures; updated after proof corrections

References in corpus (15)

• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Fractional Quantum Hall States and Jack Polynomials
• Topological Entanglement and Clustering of Jain Hierarchy States
• A nu=2/5 Paired Wavefunction
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Generalized Quantum Hall Projection Hamiltonians
• 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
• The plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries
• Second Generation of Composite Fermions in the Hamiltonian Theory
• Berry phases for composite fermions: effective magnetic field and fractional statistics
• Bridge between Abelian and Non-Abelian Fractional Quantum Hall States
• Spin phase diagram of the nu_e=4/11 composite fermion liquid
• Numerical studies of the Pfaffian model of the nu=5/2 fractional quantum Hall effect

Cited by in corpus (20)

• Quantum Hall Physics - hierarchies and CFT techniques
• Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Tripartite Composite Fermion States
• Abelian topological order of $\nu =2/5$ and $3/7$ fractional quantum Hall states in lattice models
• Solvable models for unitary and non-unitary topological phases
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• Search for exact local Hamiltonians for general fractional quantum Hall states
• Emergent Commensurability from Hilbert Space Truncation in Fractional Quantum Hall Fluids
• Gaplessness of the Gaffnian
• Effective Abelian theory from a non-Abelian topological order in $\nu =2/5$ fractional quantum Hall effect
• The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect
• Statistical interactions and boson-anyon duality in fractional quantum Hall fluids
• Gaffnian holonomy through the coherent state method
• Fractional quantum Hall effect from frustration-free Hamiltonians
• Transition from two-component 332 Halperin state to one-component Jain state at filling factor ν=2/5
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Non-quasiconvex dispersion of composite fermions and the fermionic Haffnian state in the first-excited Landau level
• Crossover from Integer to Fractional Quantum Hall Effect
• From the Gaffnian critical point to the incompressible 2/5 quantum Hall state