Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems

Abstract

The family of "Jack states" related to antisymmetric Jack polynomials are the exact zero-energy ground states of particular model short-range {\em many-body} repulsive interactions, defined by a few non-vanishing leading pseudopotentials. Some Jack states are known or anticipated to accurately describe many-electron incompressible ground states emergent from the {\em two-body} Coulomb repulsion in fractional quantum Hall effect. By extensive numerical diagonalization we demonstrate emergence of Jack states from suitable pair interactions. We find empirically a simple formula for the optimal two-body pseudopotentials for the series of most prominent Jack states generated by {\em contact} many-body repulsion. Furthermore, we seek realization of arbitrary Jack states in realistic quantum Hall systems with Coulomb interaction, i.e., in partially filled lowest and excited Landau levels in quasi-two-dimensional layers of conventional semiconductors like GaAs or in graphene.

arXiv comment12 pages, 11 figures

References in corpus (26)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Fractional Quantum Hall States and Jack Polynomials
• A nu=2/5 Paired Wavefunction
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Cooper Instability of Composite Fermions
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
• Generalized Quantum Hall Projection Hamiltonians
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Role of exciton screening in the 7/3 fractional quantum Hall effect
• Transition from Abelian to non-Abelian quantum liquids in the second Landau level
• Electron Correlations in Partially Filled Lowest and Excited Landau Levels
• Composite Fermions and quantum Hall systems: Role of the Coulomb pseudopotential
• Composite Fermions and the Fractional Quantum Hall Effect: Essential Role of the Pseudopotential
• Hund's Rule for Monopole Harmonics, or Why the Composite Fermion Picture Works
• Parafermion Statistics and Quasihole Excitations for the Generalizations of the Paired Quantum Hall States
• From Irrational to Non-Unitary: on the Haffnian and Haldane-Rezayi wave functions
• Composite Fermion Approach to the Quantum Hall Hierarchy: When it Works and Why
• Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect
• The Hierarchy of Incompressible Fractional Quantum Hall States
• Surprising robustness of particle-hole symmetry for composite fermion liquids
• Jack polynomial fractional quantum Hall states and their generalizations
• Three-body correlations and finite-size effects in the Moore--Read states on a sphere
• Unified Fock space representation of fractional quantum Hall states

Cited by in corpus (20)

• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• Abelian topological order of $\nu =2/5$ and $3/7$ fractional quantum Hall states in lattice models
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Automatic design of Hamiltonians
• 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 $\nu =2+\frac{4}{11}$
• Parametrization and thermodynamic scaling of pair correlation functions for the Fractional Quantum Hall Effect
• 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
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Mean field approximations for short range four body interactions at $\nu =3/5$
• Non-quasiconvex dispersion of composite fermions and the fermionic Haffnian state in the first-excited Landau level