Building on the growing evidence based on NMR, magnetization, neutron scattering, electron spin resonance, and specific heat that, under pressure, SrCu 2 (BO 3 ) 2 has an intermediate phase between the dimer and the Néel phase, we study the competition between two candidate phases in the context of a minimal model that includes two types of intra-and interdimer interactions without enlarging the unit cell. We show that the empty plaquette phase of the Shastry-Sutherland model is quickly replaced by a quasi-one-dimensional full plaquette phase when intra-and/or interdimer couplings take different values, and that this full plaquette phase is in much better agreement with available experimental data than the empty plaquette one.

We provide numerical evidence in favor of spontaneous chiral symmetry breaking and the concomitant appearance of an Abelian chiral spin liquid for three-component fermions on the triangular lattice described by an SU(3) symmetric Hubbard model with hopping amplitude −t (t > 0) and on-site interaction U . This chiral phase is stabilized in the Mott phase with one particle per site in the presence of a uniform π-flux per plaquette, and in the Mott phase with two particles per site without any flux. Our approach relies on effective spin models derived in the strong-coupling limit in powers of t/U for general SU(N ) and arbitrary uniform charge flux per plaquette, which are subsequently studied using exact diagonalizations and variational Monte Carlo simulations for N = 3, as well as on exact diagonalizations of the SU(3) Hubbard model on small clusters. Up to third order in t/U , and for the time-reversal symmetric cases (flux 0 or π), the low-energy description is given by the J-K model with Heisenberg coupling J and real ring exchange K. The phase diagram in the full J-K parameter range contains, apart from three already known, magnetically long-range ordered phases, two previously unreported phases: i) a lattice nematic phase breaking the lattice rotation symmetry and ii) a spontaneous timereversal and parity symmetry breaking Abelian chiral spin liquid. For the Hubbard model, an investigation that includes higher-order itinerancy effects supports the presence of a phase transition inside the insulating region, occurring at (t/U )c ≈ 0.07 [(U/t)c ≈ 13] between the three-sublattice magnetically ordered phase at small t/U and this Abelian chiral spin liquid. arXiv:1802.03179v2 [cond-mat.str-el]

We introduce a quantum spin-1/2 model hosting two exact plaquette singlet ground states in extended parameter regimes. There is an exact phase transition between both phases, at which the system has an extensive ground-state degeneracy. Further, the model exhibits an extensive number of conserved quantities, which allow the prediction of additional phases. We exploit this feature and explore the phase diagram in detail for two specific parameter regimes. The model is based solely on Heisenberg interactions and seems sufficiently simple to be realized in quantum materials. A general scheme to determine exact singlet product states is briefly discussed. (a) 1 J J v J h J (b) 1 0 2 4 1 3 pyramid plaquette p J 2 J v 2 J h 2 arXiv:1912.09060v1 [cond-mat.str-el]