Didier Poilblanc, Norbert Schuch, David Pérez-García, J. Ignacio Cirac
We investigate the relations between bulk and boundary properties of short-range resonating valence bond wave functions using Projected Entangled Pair States. We show that, for a bipartition, the boundary Hamiltonian defined on the edge can be written as a product of a highly non-local projector, which fundamentally depends upon boundary conditions, with an emergent (local) one-dimensional (superfluid) t--J Hamiltonian, which arises due to the symmetry properties of the auxiliary spins at the edge. This multiplicative structure, a consequence of the disconnected topological sectors in the space of dimer lattice coverings, is then characteristic of the topological nature of the states. For systems with open boundary conditions, it is shown that the entanglement spectrum, which reflects the properties of the (gapped or gapless) edge modes, is a subset of the spectrum of the local Hamiltonian, also explaining the origin of the topological entanglement entropy. We propose to use these features to probe topological phases in microscopic Hamiltonians.
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http://arxiv.org/abs/1202.0947
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