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 $ϕ_n^m$ parton states can be expressed as the conformal blocks of the $U(1) \otimes SU(n)_m$ WZW models.