# Groupe de Physique Statistique

## Equipe 106, Institut Jean Lamour

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### Articles dans des revues à comité de lecture

 Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension Dubail J., Read N. Phys. Rev B 92 (2016) 205307 DOI : 10.1103/PhysRevB.92.205307 ArXiv : arxiv:1307.7726 [PDF] Trial wavefunctions that can be represented by summing over locally-coupled degrees of freedom are called tensor network states (TNSs); 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, in the sense that the fermionic excitations live in a topologically non-trivial bundle of the required type. We prove that any strictly short-range quadratic parent Hamiltonian for these states is gapless; the proof holds for a class of systems in any dimension of space. The proof also shows, quite generally, that sets of compactly-supported Wannier-type functions do not exist for band structures in this class. We construct further examples of TNSs that are analogs of fractional (including non-Abelian) quantum Hall phases; it is not known whether parent Hamiltonians for these are also gapless.