Exactly solvable Hamiltonian for the chiral spin liquid

An exact spin Hamiltonian for the chiral spin liquid will be presented. The model starts with the quantum Hall wave function on a lattice of N sites in a toroidal geometry, a state that describes a spin liquid that violates the symmetries of parity and time reversal. A parent Hamiltonian for which the state is the exact ground state is constructed out of vector operators that annihilate the ground state. This model avoids the subtle error that has been identified [D. F. Schroeter, Ann. Phys. \textbf {310}, 155 (2004)] in Laughlin's original solution to the problem [R. B. Laughlin, Ann. Phys. \textbf{191}, 163 (1989)]. The construction of the model and its numerical verification will be presented.