Edge states for the Kalmeyer-Laughlin wave function

TL;DR

This paper investigates lattice wave functions derived from conformal field theory, demonstrating their edge state properties, their relation to low-energy excitations, and deriving parent Hamiltonians for certain states.

Contribution

It introduces a method to construct and analyze edge states from the Kalmeyer-Laughlin wave function using conformal field theory and numerical simulations.

Findings

Edge states are identified via correlation functions.

Low-energy states have high overlap with edge states.

Parent Hamiltonians with SU(2) symmetry are derived.

Abstract

We study lattice wave functions obtained from the SU(2)$_1$ Wess-Zumino-Witten conformal field theory. Following Moore and Read's construction, the Kalmeyer-Laughlin fractional quantum Hall state is defined as a correlation function of primary fields. By an additional insertion of Kac-Moody currents, we associate a wave function to each state of the conformal field theory. These wave functions span the complete Hilbert space of the lattice system. On the cylinder, we study global properties of the lattice states analytically and correlation functions numerically using a Metropolis Monte Carlo method. By comparing short-range bulk correlations, numerical evidence is provided that the states with one current operator represent edge states in the thermodynamic limit. We show that the edge states with one Kac-Moody current of lowest order have a good overlap with low-energy excited states of a local Hamiltonian, for which the Kalmeyer-Laughlin state approximates the ground state. For some states, exact parent Hamiltonians are derived on the cylinder. These Hamiltonians are SU(2) invariant and nonlocal with up to four-body interactions.