Parent Hamiltonian for the Chiral Spin Liquid

TL;DR

This paper develops a method to construct parent Hamiltonians for the chiral spin liquid, identifying two Hamiltonians where the chiral spin liquid is an exact ground state, and analyzing their spectral properties.

Contribution

It introduces a novel approach to derive parent Hamiltonians for the chiral spin liquid and distinguishes their ground state degeneracies on a square lattice.

Findings

One Hamiltonian has a unique ground state matching the chiral spin liquid.

The other Hamiltonian's ground state is degenerate.

Numerical diagonalization confirms the ground state properties.

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 two-fold topological degeneracy, is indeed the unique ground state for one Hamiltonian, while it is not unique for the other.