Bosonic fractional quantum Hall states on the torus from conformal field theory

Abstract

The Kalmeyer-Laughlin state, which is a lattice version of the bosonic Laughlin state at filling factor one half, has attracted much attention due to its topological and chiral spin liquid properties. Here we show that the Kalmeyer-Laughlin state on the torus can be expressed in terms of a correlator of conformal fields from the $SU(2{)}_1$ Wess-Zumino-Witten model. This reveals an interesting underlying mathematical structure and provides a natural way to generalize the Kalmeyer-Laughlin state to arbitrary lattices on the torus. We find that the many-body Chern number of the states is unity for more different lattices, which suggests that the topological properties of the states are preserved when the lattice is changed. Finally, we analyze the symmetry properties of the states on square lattices.

25 pages, 5 figures, v2: accepted version

References in corpus (5)

• Fractional Quantum Hall Effect in Optical Lattices
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$
• Projected BCS states and spin Hamiltonians for the SO(n)_1 Wess-Zumino-Witten model
• Transitions Between Chiral Spin Liquids and Z2 Spin Liquids

Cited by in corpus (11)

• Equipartition of the Entanglement Entropy
• Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice
• Spin Correlations and Topological Entanglement Entropy in a Non-Abelian Spin-1 Spin Liquid
• Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
• Edge states for the Kalmeyer-Laughlin wave function
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Matrix product approximations to multipoint functions in two-dimensional conformal field theory
• Matrix product approximations to conformal field theories
• Conformal field theory and the non-abelian $SU(2{)}_k$ chiral spin liquid
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Chain and ladder models with two-body interactions and analytical ground states