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Poilblanc, Didier and Schuch, Norbert and Pérez García, David and Cirac, J. Ignacio (2012) Topological and entanglement properties of resonating valence bond wave functions. Physical Review B, 86 (1). ISSN 10980121

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Official URL: http://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.014404
Abstract
We examine in details the connections between topological and entanglement properties of shortrange resonating valence bond (RVB) wave functions using projected entangled pair states (PEPS) on kagome and square lattices on (quasi)infinite cylinders with generalized boundary conditions (and perimeters with up to 20 lattice spacings). By making use of disconnected topological sectors in the space of dimer lattice coverings, we explicitly derive (orthogonal) “minimally entangled” PEPS RVB states. For the kagome lattice, using the quantum Heisenberg antiferromagnet as a reference model, we obtain the finitesize scaling with increasing cylinder perimeter of the vanishing energy separations between these states. In particular, we extract two separate (vanishing) energy scales corresponding (i) to insert a vison line between the two ends of the cylinder and (ii) to pull out and freeze a spin at either end. We also investigate the relations between bulk and boundary properties and show that, for a bipartition of the cylinder, the boundary Hamiltonian defined on the edge can be written as a product of a highly nonlocal projector, which fundamentally depends upon boundary conditions, with an emergent (local) SU(2)invariant onedimensional (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 characteristic of the topological nature of the states. For minimally entangled RVB states, it is shown that the entanglement spectrum, which reflects the properties of the (gapless or gapped) edge modes, is a subset of the spectrum of the local Hamiltonian, e.g., half of it for the kagome RVB state, providing a simple argument on the origin of the topological entanglement entropy S0 = −ln 2 of the Z2 spin liquid. We propose to use these features to probe topological phases in microscopic Hamiltonians, and some results are compared to existing density matrix renormalization group data.
Item Type:  Article 

Subjects:  Sciences > Physics > Mathematical physics Sciences > Physics > Quantum theory 
ID Code:  27963 
Deposited On:  13 Feb 2015 12:47 
Last Modified:  13 Feb 2015 12:47 
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