Parent Hamiltonian for the chiral spin liquid

Abstract

We present a method for constructing parent Hamiltonians for the chiral spin liquid. We find two distinct Hamiltonians for which the chiral spin liquid on a square lattice is an exact zero-energy ground state. We diagonalize both Hamiltonians numerically for 16-site lattices, and find that the chiral spin liquid, modulo its twofold topological degeneracy, is indeed the unique ground state for one Hamiltonian, while it is not unique for the other.