Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime

Abstract

In fractional quantum Hall physics, the Hilbert space is projected to a single Landau level and the entire Hamiltonian consists of just the projected inter-electron interaction. Haldane's pseudopotential formalism has been an extremely useful tool both for understanding these interactions, and for understanding the quantum Hall states that result. In the current paper we consider the analogue of this pseudopotential construction that results from general M-body interactions rather than the usual (Coulomb) two-body interaction.

Revision: one citation changed. 11+epsilon pages, 1 table, no figures

References in corpus (11)

• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Condensation of `composite bosons' in a rotating BEC
• Quantum Hall fractions in rotating Bose-Einstein condensates
• A Composite Fermion Description of Rotating Bose-Einstein Condensates
• A nu=2/5 Paired Wavefunction
• Generalized Quantum Hall Projection Hamiltonians
• Exact Groundstates of Rotating Bose Gases close to a Feshbach Resonance
• Three-body correlations and finite-size effects in the Moore--Read states on a sphere

Cited by in corpus (73)

• Non-Abelian Anyons and Topological Quantum Computation
• Topological Flat Band Models and Fractional Chern Insulators
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Quantum Hall Physics - hierarchies and CFT techniques
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Bulk-Edge Correspondence in the Entanglement Spectra
• The Effect of Landau Level-Mixing on the Effective Interaction between Electrons in the fractional quantum Hall regime
• Landau Level Mixing and the Fractional Quantum Hall Effect
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Model anisotropic quantum Hall states
• Many-Body Topological and Skin States without Open Boundaries
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Conformal invariance of chiral edge theories
• Landau Level Mixing in the Perturbative Limit
• Pseudopotential Formalism for Fractional Chern Insulators
• The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states
• Landau Level Quantization on the Sphere
• Floquet Mechanism for Non-Abelian Fractional Quantum Hall States
• Non-Abelian Fractional Chern Insulators from Long-Range Interactions
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Geometric construction of Quantum Hall clustering Hamiltonians
• Graviton Chirality and Topological Order in the Half-filled Landau Level
• The enigmatic 12/5 fractional quantum Hall effect
• Bridge between Abelian and Non-Abelian Fractional Quantum Hall States
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
• Clustering properties, Jack polynomials and unitary conformal field theories
• Phase diagram and edge states of the $\nu =5/2$ fractional quantum Hall state with Landau level mixing and finite well thickness
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• Tracing non-Abelian anyons via impurity particles
• Entanglement subspaces, trial wavefunctions, and special Hamiltonians in the fractional quantum Hall effect
• Mapping of Parent Hamiltonians: from Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains
• Topological order: from long-range entangled quantum matter to an unification of light and electrons
• S3 Quantum Hall Wavefunctions
• Search for exact local Hamiltonians for general fractional quantum Hall states
• Multi-Particle Pseudopotentials for Multi-Component Quantum Hall Systems
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Gaplessness of the Gaffnian
• Linear and nonlinear edge dynamics of trapped fractional quantum Hall droplets
• The Neutral Excitations in the Gaffnian State
• Automatic design of Hamiltonians
• Landau level quantization for massless Dirac fermions in the spherical geometry: graphene fractional quantum Hall effect on the Haldane sphere
• Statistical interactions and boson-anyon duality in fractional quantum Hall fluids
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Gaffnian holonomy through the coherent state method
• Fractional Quantum Hall Matrix Product States For Interacting Conformal Field Theories
• Hyperspherical theory of the quantum Hall effect: the role of exceptional degeneracy
• Model interactions for Pfaffian paired states based on Chern-Simons field theory description
• Microscopic Study of the Coupled-Wire Construction and Plausible Realization in Spin-Dependent Optical Lattices
• Pfaffian paired states for half-integer 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
• Magnetization and Spin Excitations of Non-Abelian Quantum Hall States
• Edge reconstruction of fractional quantum Hall liquids with spin degrees of freedom
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Thermoelectric Hall conductivity of the fractional quantum Hall systems on a disk
• Mean field approximations for short range four body interactions at $\nu =3/5$
• Spin-singlet Gaffnian wave function for fractional quantum Hall systems
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Construction of a series of new $\nu =2/5$ fractional quantum Hall wave functions by conformal field theory
• ${\mathbb{Z}}_k^{(r)}$-Algebras, FQH Ground States, and Invariants of Binary Forms
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Refermionized theory of the edge modes of a fractional quantum Hall cloud
• Torus geometry eigenfunctions of an interacting multi-Landau level Hamiltonian
• Exact Mappings in Condensed Matter Physics
• Flat bands on spherical surface: from Landau levels to giant-quantum-number orbitals
• Second-quantized approach to the study of Halperin state in fractional quantum Hall effect