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We exploit a natural projected entangled-pair state (PEPS) representation for the resonating Affleck-Kennedy- Lieb-Tasaki loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power law. On the 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 the 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 state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform a variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS. [ABSTRACT FROM AUTHOR]

Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al., Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory suggested a dimerized, color-ordered state (Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called bond dimension D. Both competing states can be reproduced with iPEPS by using different unit cell sizes. For small D the dimer state has a lower variational energy than the plaquette state; however, for large D it is the latter which becomes energetically favorable. The plaquette formation is also confirmed by exact diagonalizations and variational Monte Carlo studies, according to which both the dimerized and plaquette states are nonchiral flux states. [ABSTRACT FROM AUTHOR]

We present a numerical study of the SU(N) Heisenberg model with the fundamental representation at each site for the kagome lattice (for N = 3) and the checkerboard lattice (for N = 4), which are the line graphs of the honeycomb and square lattices and thus belong to the class of bisimplex lattices. Using infinite projected entangled-pair states and exact diagonalizations, we show that in both cases the ground state is a simplex solid state with a twofold degeneracy, in which the N spins belonging to a simplex (i.e., a complete graph) form a singlet. Theses states can be seen as generalizations of valence bond solid states known to be stabilized in certain SU(2) spin models. [ABSTRACT FROM AUTHOR]

The competition between Kitaev and Heisenberg interactions away from half filling is studied for the hole-doped Kitaev-Heisenberg t-JK-JH model on a honeycomb lattice. While the isotropic Heisenberg coupling supports a time-reversal violating d-wave singlet state, we find that the Kitaev interaction favors a time-reversal invariant p-wave superconducting phase, which obeys the rotational symmetries of the microscopic model, and is robust for JH < JK/2. Within the p-wave superconducting phase, a critical chemical potential |μ| = μc &ap; t separates a topologically trivial phase for |μ| < μc from a topologically nontrivial Z2 time-reversal invariant spin-triplet phase for |μ| > μc. [ABSTRACT FROM AUTHOR]

Combining thermodynamic measurements with theoretical calculations we demonstrate that the iridates A2Ir03 (A = Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S=1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from &thetas; = --125 K for Na2Ir03 to &thetas; &thkap; --33 K for Li2Ir03, while the ordering temperature remains roughly the same TN &thkap; 15 K. Using functional renormalization group calculations we show that this evolution of &thetas; and TN as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na2Ir03 is deep in a magnetically ordered regime, while Li2Ir03 appears to be close to a spin-liquid regime. [ABSTRACT FROM AUTHOR]