Matrix Product State Description and Gaplessness of the Haldane-Rezayi State

Abstract

We derive an exact matrix product state representation of the Haldane-Rezayi state on both the cylinder and torus geometry. Our derivation is based on the description of the Haldane-Rezayi state as a correlator in a non-unitary logarithmic conformal field theory. This construction faithfully captures the ten degenerate ground states of this model state on the torus. Using the cylinder geometry, we probe the gapless nature of the phase by extracting the correlation length, which diverges in the thermodynamic limit. The numerically extracted topological entanglement entropies seem to only probe the Abelian part of the theory, which is reminiscent of the Gaffnian state, another model state deriving from a non-unitary conformal field theory.

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References in corpus (47)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Area laws in quantum systems: mutual information and correlations
• $2n$ 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
• Entropy scaling and simulability by Matrix Product States
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• Bits and Pieces in Logarithmic Conformal Field Theory
• Quantum Hall Physics - hierarchies and CFT techniques
• Symplectic Fermions
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Edge excitations of paired fractional quantum Hall states
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Exact Matrix Product States for Quantum Hall Wave Functions
• Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model
• A nu=2/5 Paired Wavefunction
• Charge-Spin Separation and the Spectral Properties of Luttinger Liquids
• Real-Space Entanglement Spectrum of Quantum Hall States
• The Ground State Structure and Modular Transformations of Fractional Quantum Hall States on a Torus
• Real-space entanglement spectrum of quantum Hall systems
• Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions
• The Haldane-Rezayi Quantum Hall State and Conformal Field Theory
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• A Unified Conformal Field Theory Description of Paired Quantum Hall States
• Quantum Hall quasielectron operators in conformal field theory
• Hall Viscosity of Hierarchical Quantum Hall States
• Relating c<0 and c>0 Conformal Field Theories
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Gapless excitations in the Haldane-Rezayi state: The thin torus limit
• Model States for a Class of Chiral Topological Order Interfaces
• Hierarchy wave functions--from conformal correlators to Tao-Thouless states
• From Irrational to Non-Unitary: on the Haffnian and Haldane-Rezayi wave functions
• Matrix Product State description of the Halperin States
• Matrix product state representation of non-Abelian quasiholes
• A general approach to quantum Hall hierarchies
• Half-Integral Spin-Singlet Quantum Hall Effect
• Gaplessness of the Gaffnian
• Modified Coulomb gas construction of quantum Hall states from non-unitary conformal field theories
• Topological d-wave pairing structures in Jain states
• Existence of strong-pairing quantum Hall phase in bilayer cold atom systems with dipolar interactions
• Connected components of irreducible maps and 1D quantum phases
• A Novel CFT Approach to Bulk Wave Functions in the Fractional Quantum Hall Effect
• Electron and Quasiparticle Exponents of Haldane-Rezayi state in Non-abelian Fractional Quantum Hall Theory
• Pairing symmetry transitions in the even-denominator FQHE system

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