Entangled Pauli Principles: the DNA of Quantum Hall Fluids

Abstract

A formalism is developed for the rigorous study of solvable fractional quantum Hall parent Hamiltonians with Landau level mixing. The idea of organization through "generalized Pauli principles" is expanded to allow for root level entanglement, giving rise to "entangled Pauli principles". Through the latter, aspects of the effective field theory description become ingrained in exact microscopic solutions for a great wealth of phases for which no similar single Landau level description is known. We discuss in detail braiding statistic, edge theory, and rigorous zero mode counting for the Jain-221 state as derived from a microscopic Hamiltonian. The relevant root-level entanglement is found to feature an AKLT-type MPS structure associated with an emergent SU(2) symmetry.

arXiv comment12 pages, including supplemental. Revised version includes two references corresponding to multi-layer graphene

References in corpus (47)

• Non-Abelian Anyons and Topological Quantum Computation
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Geometrical Description of the Fractional Quantum Hall Effect
• Fractional Quantum Hall States and Jack Polynomials
• Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
• Edge excitations of paired fractional quantum Hall states
• Exact Parent Hamiltonian for the Quantum Hall States in a Optical Lattice
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Incompressible Quantum Liquids and New Conservation Laws
• Algebraic Approach to Interacting Quantum Systems
• Exact Matrix Product States for Quantum Hall Wave Functions
• Abelian and Non-abelian Hall Liquids and Charge Density Wave: Quantum Number Fractionalization in One and Two Dimensions
• A nu=2/5 Paired Wavefunction
• Projective Construction of Non-Abelian Quantum Hall Liquids
• Quantum Hall Effects in Graphene-Based Two-Dimensional Electron Systems
• The Pfaffian quantum Hall state made simple--multiple vacua and domain walls on a thin torus
• One-Dimensional Theory of the Quantum Hall System
• The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
• Conformal invariance of chiral edge theories
• Matrix Product States for Trial Quantum Hall States
• Pseudopotential Formalism for Fractional Chern Insulators
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states
• Halperin (m, m',n) bilayer quantum Hall states on thin cylinders
• Repulsive Interactions in Quantum Hall Systems as a Pairing Problem
• S-duality constraints on 1D patterns associated with fractional quantum Hall states
• Gapless excitations in the Haldane-Rezayi state: The thin torus limit
• Domain wall type defects as anyons in phase space
• Pfaffian statistics through adiabatic transport in the 1D coherent state representation
• Composite Fermions on a Torus
• Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
• Abelian and non-Abelian statistics in the coherent state representation
• The Jain-2/5 parent Hamiltonian: structure of zero modes, dominance patterns, and zero mode generators
• Algebraic approach to the study of zero modes of Haldane pseudopotentials
• Thin torus perturbative analysis of elementary excitations in the Gaffnian and Haldane-Rezayi quantum Hall states
• Momentum resolved tunneling into the Pfaffian and anti-Pfaffian edges
• Multi-Particle Pseudopotentials for Multi-Component Quantum Hall Systems
• The Neutral Excitations in the Gaffnian State
• Gaffnian holonomy through the coherent state method
• Bounds for low-energy spectral properties of center-of-mass conserving positive two-body interactions

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• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
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• 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
• Local two-body parent Hamiltonians for the entire Jain sequence
• Composite fermion pairing induced by Landau level mixing
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Search for exact local Hamiltonians for general fractional quantum Hall states
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Theoretical phase diagram of two-component composite fermions in double layer graphene
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Composite fermions in Fock space: Operator algebra, recursion relations, and order parameters
• Adiabatic Construction of Hierarchical Quantum Hall States
• An Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids
• Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods
• Interaction-driven quantum phase transitions between topological and crystalline orders of electrons
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Torus geometry eigenfunctions of an interacting multi-Landau level Hamiltonian
• Candidate local parent Hamiltonian for 3/7 fractional quantum Hall effect