Changes and additions to the new edition of this classic textbook include a new chapter on symmetries, new problems and examples, improved explanations, more numerical problems to be worked on a computer, new applications to solid state physics, and consolidated treatment of time-dependent potentials.

We construct a Hamiltonian that singles out the chiral spin liquid on a square lattice with periodic boundary conditions as the exact and, apart from the twofold topological degeneracy, unique ground state.

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.

We construct a parent Hamiltonian for the family of non-Abelian chiral spin liquids proposed recently by two of us [PRL 102, 207203 (2009)], which includes the Abelian chiral spin liquid proposed by Kalmeyer and Laughlin, as the special case S=1/2. As we use a circular disk geometry with an open boundary, both the annihilation operators we identify and the Hamiltonians we construct from these are exact only in the thermodynamic limit.Comment: 5+2 pages, no figures. Version 2: two references adde

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