Tensor network trial states for chiral topological phases in two dimensions
Trial wavefunctions that can be represented by summing over locally-coupled degrees of freedom are called tensor network states; they have seemed difficult to construct for two-dimensional topological phases that possess protected gapless edge excitations. We show it can be done for chiral states of free fermions, using a Gaussian Grassmann integral, yielding p_x \pm i p_y and Chern insulator states. We show that any strictly short-range quadratic parent Hamiltonian for these states is gapless. Further examples are analogs of fractional (including non-Abelian) quantum Hall phases.