Trial wave functions for quantum Hall edge states

Jérôme Dubail, N. Read, Edward H. Rezayi

De Filippo S, Carmine Lubritto

Trial wave functions for Laughlin's liquids in the presence of confining potentials are considered. They lead to a description of fractional quantum Hall edge states as a prototype of the chiral Luttinger liquid. Their reliability is confirmed by Monte Carlo simulation of the equivalent classical plasma. © 1999 Elsevier Science B.V. All rights reserved.

Greg J. Henderson, G. J. Sreejith, Steven H. Simon

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 (assuming that the corresponding chiral algebra does indeed define a physically “sensible” CFT). A field-theoretic generalization of Laughlin's plasma analogy, known as generalized screening, is formulated for these states. If this holds, along with an additional assumption, 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, generalizing the result of Dubail [], which implies the equality between edge-state and entanglement level counting to state counting in the corresponding CFT. We numerically test this result in the case of the unprojected ν=2/5 composite fermion state and the bosonic ν=1ϕ22 parton state. We discuss how Read's arguments [] still apply, implying that conformal blocks of the CFT defined by the corresponding chiral algebra are valid quasihole trial wave functions, with the adiabatic braiding statistics given by the monodromy of these functions, assuming the existence of a quasiparticle trapping Hamiltonian. Generalizations of these constructions are discussed, with particular attention given to simple current constructions. It is shown that all chiral composite fermion wave functions can be expressed as CFT correlation functions without explicit symmetrization or antisymmetrization and that the ground, edge, and certain quasihole trial wave functions of the ϕnm parton states can be expressed as the conformal blocks of the U(1)⊗SU(n)m WZW models. Finally, we discuss the relation of the ϕ2k series with the Read-Rezayi series, where several examples of quasihole braiding statistics calculations are given. Published by the American Physical Society 2024

Jérôme Dubail, N. Read, Edward H. Rezayi

We consider the trial wave functions for the fractional quantum Hall effect that are given by conformal blocks, and construct their associated edge excited states in full generality. The inner products between these edge states are computed in the thermodynamic limit, assuming generalized screening (i.e., short-range correlations only) inside the quantum Hall droplet and using the language of boundary conformal field theory (boundary CFT). These inner products take universal values in this limit: they are equal to the corresponding inner products in the bulk two-dimensional chiral CFT which underlies the trial wave function. This is a bulk/edge correspondence; it shows the equality between equal-time correlators along the edge and the correlators of the bulk CFT up to a Wick rotation. This approach is then used to analyze the entanglement spectrum of the ground state obtained with a bipartition $A\ensuremath{\cup}B$ in real space. Starting from our universal result for inner products in the thermodynamic limit, we tackle corrections to scaling using standard field-theoretic and renormalization-group arguments. We prove that generalized screening implies that the entanglement Hamiltonian ${H}_{E}=\ensuremath{-}\mathrm{ln}{\ensuremath{\rho}}_{A}$ is isospectral to an operator that is local along the cut between $A$ and $B$. We also show that a similar analysis can be carried out for particle partition. We discuss the close analogy between the formalism of trial wave functions given by conformal blocks and tensor product states, for which results analogous to ours have appeared recently. Finally, the edge theory and entanglement spectrum of ${p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$ paired superfluids are treated in a similar fashion in the Appendixes.

Jennifer Cano, Meng Cheng, Michael Mulligan +3 more