Laughlin spin liquid states on lattices obtained from conformal field theory

TL;DR

This paper introduces lattice spin wavefunctions inspired by Laughlin states, derived from conformal field theory, and presents a parent Hamiltonian generalizing the Haldane-Shastry model, with connections to the Kalmeyer-Laughlin state.

Contribution

It constructs lattice Laughlin-like spin wavefunctions from conformal blocks and provides a parent Hamiltonian generalizing the Haldane-Shastry model for any even number of spins.

Findings

Reproduces Laughlin states on lattices

Derives a parent Hamiltonian valid for any even number of spins

Shows the Kalmeyer-Laughlin state as a special case

Abstract

We propose a set of spin system wavefunctions that are very similar to lattice versions of the Laughlin states. The wavefunction are conformal blocks of conformal field theories, and for filling factor \nu=1/2 we provide a parent Hamiltonian, which is valid for any even number of spins and is at the same time a 2D generalization of the Haldane-Shastry model. We also demonstrate that the Kalmeyer-Laughlin state is reproduced as a particular case of this model. Finally, we discuss various properties of the spin states and point out several analogies to known results for the Laughlin states.