Fractional Quantum Hall Matrix Product States For Interacting Conformal Field Theories

Abstract

Using truncated conformal field theory (CFT), we present the formalism necessary to obtain exact matrix product state (MPS) representations for any fractional quantum hall model state which can be written as an expectation value of primary fields in some conformal field theory. The auxiliary bond space is the Hilbert space of the descendants of primary fields and matrix elements can be calculated using well-known CFT commutation relations. We obtain a site-independent MPS representation on the thin annulus and cylinder, while a site-dependent representation is possible on the disk and sphere geometries. We discuss the complications that arise due to the presence of null vectors in the theory's Hilbert space, and present an array of procedures which optimize the numerical calculation of matrix elements. By truncating the Hilbert space of the CFT, we then build an approximate MPS representation for Laughlin, Moore-Read, Read-Rezayi, Gaffnian, minimal $M(3,r+2)$ models, and a series of superconformal minimal models. We show how to obtain, in the MPS representation, the Orbital, Particle, and Real Space entanglement spectrum in both the finite and infinite systems.

arXiv comment82 pages, 9 figures

References in corpus (30)

• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entropy and Area
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Fractional Quantum Hall States and Jack Polynomials
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• The entanglement gap and a new principle of adiabatic continuity
• Renormalization group transformations on quantum states
• New Class of Non-Abelian Spin-Singlet Quantum Hall States
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Extracting Excitations From Model State Entanglement
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• Disentangling Entanglement Spectra of Fractional Quantum Hall States on Torus Geometries
• Exact Matrix Product States for Quantum Hall Wave Functions
• Topological Entanglement and Clustering of Jain Hierarchy States
• Real-Space Entanglement Spectrum of Quantum Hall States
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Real-space entanglement spectrum of quantum Hall systems
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• 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
• Evaluation of ranks of real space and particle entanglement spectra for large systems
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Entanglement signatures of quantum Hall phase transitions
• Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
• Hierarchy wave functions--from conformal correlators to Tao-Thouless states
• Clustering properties, Jack polynomials and unitary conformal field theories
• Entanglement subspaces, trial wavefunctions, and special Hamiltonians in the fractional quantum Hall effect
• The third parafermionic chiral algebra with the symmetry Z_{3}

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• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Model States for a Class of Chiral Topological Order Interfaces
• Matrix product approximations to conformal field theories
• Field Tensor Network States
• Conformal field theory construction for nonabelian hierarchy wave functions