Crossover from Integer to Fractional Quantum Hall Effect

Abstract

The parton theory constructs candidate fractional quantum Hall states by decomposing the physical particles into unphysical partons, placing the partons in integer quantum Hall states, and then gluing the partons back into the physical particles. Field theoretical formulations execute the gluing process through the device of emergent gauge fields. Here we study numerically the process of going from the integer quantum Hall effect of two species of fermionic partons to the fractional quantum Hall effect of bosons by introducing an attractive interaction between the fermions of different species and continuously increasing its strength to glue them into bosons. To properly capture the physics in the bulk, we implement this process in a lattice version of the spherical geometry, which allows us to keep the full Hilbert space. Even though the two end-point states are topologically distinct, we find that, for the small system sizes accessible to our study, the energy gap remains open, indicating a crossover between these two states.

11 pages, 8 figures

References in corpus (33)

• Observation of resonance condensation of fermionic atom pairs
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• BCS-BEC Crossover and the Unitary Fermi Gas
• 1/2-Anyons in small atomic Bose-Einstein condensates
• Realization of a fractional quantum Hall state with ultracold atoms
• A nu=2/5 Paired Wavefunction
• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• Quantization of Hall Conductance For Interacting Electrons on a Torus
• Parton construction of a wave function in the anti-Pfaffian phase
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Sum Rule of the Hall Conductance in Random Quantum Phase Transition
• Many-body Chern number without integration
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Insensitivity of bulk properties to the twisted boundary condition
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Fractional angular momentum in cold atom systems
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Creating a bosonic fractional quantum Hall state by pairing fermions
• Quantum Hall Transition near a Fermion Feshbach Resonance in a Rotating Trap
• Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect
• Effective Abelian theory from a non-Abelian topological order in $\nu =2/5$ fractional quantum Hall effect
• Adiabatic Construction of Hierarchical Quantum Hall States
• Composite anyons on a torus
• Adiabatic Heuristic Principle on a Torus and Generalized Streda Formula
• Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle
• Adiabatic Continuity of the Spinful Quantum Hall States
• Superconductivity in a system of interacting spinful semions