RT Journal Article
T1 Topological and entanglement properties of resonating valence bond wave functions
A1 Poilblanc, Didier
A1 Schuch, Norbert
A1 Pérez García, David
A1 Cirac, J. Ignacio
AB We examine in details the connections between topological and entanglement properties of short-range 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 finite-size 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 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 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.
PB American Physical Society
SN 1098-0121
YR 2012
FD 2012-07-06
LK https://hdl.handle.net/20.500.14352/44444
UL https://hdl.handle.net/20.500.14352/44444
LA eng
NO Comunidad de Madrid
NO Ministerio de Ciencia e Innovación (MICINN)
NO Unión Europea. FP7
NO Agence Nationale de la Recherche
NO CALMIP
NO NSF
DS Docta Complutense
RD 8 abr 2025