Conformal field theory approach to parton fractional quantum Hall trial wave functions

Abstract

We show that all lowest Landau level projected and unprojected chiral parton type fractional quantum Hall ground and edge state trial wave functions, which take the form of products of integer quantum Hall wave functions, can be expressed as conformal field theory (CFT) correlation functions, where we can associate a chiral algebra to each parton state such that the CFT defined by the algebra is the ``smallest'' such CFT that can generate the corresponding ground and edge state trial wave functions. A field-theoretic generalisation of Laughlin's plasma analogy, known as generalised screening, is formulated for these states. If this holds, we argue that the inner products of edge state trial wave functions, for parton states where the ``densest'' trial wave function is unique, can be expressed as matrix elements of an exponentiated local action operator of the CFT, generalising the result of Dubail et al. [PRB 85, 11531 (2012)], which implies the equality between edge state and entanglement level counting to state counting in the corresponding CFT. We numerically test this result in two specific cases. We discuss how Read's arguments [PRB 79, 045308 (2009)] still apply, implying that conformal blocks of the CFT defined by the corresponding chiral algebra are valid quasi-hole trial wave functions, with the adiabatic braiding statistics given by the monodromy of these functions, assuming the existence of a quasi-particle trapping Hamiltonian. Generalisations of these constructions are discussed. It is shown that all chiral composite fermion wave functions can be expressed as CFT correlation functions without explicit symmetrisation or anti-symmetrisation and that the ground, edge, and certain quasi-hole trial wave functions of the ${\varphi }_n^m$ parton states can be expressed as the conformal blocks of the $U(1)\otimes SU(n{)}_m$ WZW models.

64 pages, 8 figures, 10 tables

References in corpus (17)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Topological Entanglement in Abelian and non-Abelian Excitation Eigenstates
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• 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
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• How SU(2)${}_4$ Anyons are Z${}_3$ Parafermions
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence

Cited by in corpus (6)

• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Non-Abelian phases from the condensation of Abelian anyons
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids