Rokhsar-Kivelson models of bosonic symmetry-protected topological states

A platform for constructing microscopic Hamiltonians describing bosonic symmetry-protected topological (SPT) states is presented. The Hamiltonians we consider are examples of frustration-free Rokhsar-Kivelson models, which are known to be in one-to-one correspondence with classical stochastic systems in the same spatial dimensionality. By exploring this classical-quantum mapping, we are able to construct a large class of microscopic models which, in a closed manifold, have a nondegenerate gapped symmetric ground state describing the universal properties of SPT states. Examples of one- and two-dimensional SPT states which illustrate our approach are discussed.