Tuesday, February 7, 2012
Institute for Quantum Information Seminar
Understanding RVB states with PEPS
David Perez-Garcia, Associate Professor, Mathematical Analysis, Complutense University of Madrid
Using the Projected Entangled Pair State (PEPS) toolbox, we are able to map the Resonating Valence Bond State (RVB) in a Kagome lattice in the Quantum Dimer Model (QDM) to the toric code in a square lattice. This (i) gives a local Hamiltonian for the QDM-RVB with degeneracy 4 (which in addition can be chosen to be gapped or gapless) and (ii) gives a clear picture of the excitations and topological character of the RVB. Moreover, the same map gives (i) and (ii) for the SU(2)-RVB and allows to interpolate between the two (QDM-RVB and SU(2)-RVB). Numerical calculations using also the PEPS toolbox suggest the presence of a phase transition along this path. We will show finally how thePEPS picture of the SU(2)-RVB can help in designing ways of engineering it in a quantum computer.