Edge states for the Kalmeyer-Laughlin wave function

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.

17 pages, 8 figures, 3 tables; v4: error bars and fig. 6 corrected + minor corrections

References in corpus (6)

• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Non-Abelian Statistics in a Quantum Antiferromagnet
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Excited States in Spin Chains from Conformal Blocks

Cited by in corpus (7)

• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Many-body Lattice Wavefunctions From Conformal Blocks
• Properties of Laughlin states on fractal lattices
• The BCS wave function, matrix product states, and the Ising conformal field theory