Topological Order in the Projected Entangled-Pair States Formalism: Transfer Operator and Boundary Hamiltonians

Norbert Schuch (1) , Didier Poilblanc (2, 3) , J. Ignacio Cirac (4) , David Perez-Garcia

1 Institute for Quantum Information
2 FFC - Fermions Fortement Corrélés (LPT)
3 LPT - Laboratoire de Physique Théorique
4 MPQ - Max-Planck-Institut für Quantenoptik

In the ground state of a gapped spin system, the physical properties of a region of the bulk are encoded in a Hamiltonian that lives on its boundary. We study the structure of such boundary Hamiltonians for topological models in the framework of Projected Entangled Pair States (PEPS). We find that the boundary Hamiltonian decomposes into two parts: A universal part which is entirely non-local but independent of microscopic details, encoding the nature of the topological phase, and a non-universal part which is local and depends on microscopic details only. A topological phase transition is reflected by a diverging interaction length of the non-universal part.

Domaines: Autre [cond-mat.other]; Physique Quantique [quant-ph]

Norbert Schuch, Didier Poilblanc, J. Ignacio Cirac, David Perez-Garcia. Topological Order in the Projected Entangled-Pair States Formalism: Transfer Operator and Boundary Hamiltonians. Physical Review Letters, 2013, 111, pp.090501. ⟨10.1103/PhysRevLett.111.090501⟩. ⟨hal-00744396⟩