QUROPE Quantum Information Processing and Communication in Europe

We exploit a natural Projected Entangled-Pair State (PEPS) representation for the resonating AKLT-loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional (2D) lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power-law. On kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid. We provide further evidence that the RAL state on kagome lattice is a Z2 spin liquid, by identifying the four topological sectors and computing the topological entropy. Furthermore, we construct a one-parameter family of PEPS states interpolating between the RAL state and a short-range Resonating Valence Bond (RVB) state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS.