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 investigate the minus-sign problem that afflicts quantum Monte Carlo (QMC) simulations of frustrated quantum spin systems, focusing on spin S = 1/2, two spatial dimensions, and the extended Shastry-Sutherland model. We show that formulating the Hamiltonian in the diagonal dimer basis leads to a sign problem that becomes negligible at low temperatures for small and intermediate values of the ratio of the inter-and intra-dimer couplings. This is a consequence of the fact that the product state of dimer singlets is the exact ground state both of the extended Shastry-Sutherland model and of a corresponding "sign-problem-free" model, obtained by changing the signs of all positive off-diagonal matrix elements in the dimer basis. By exploiting this insight, we map the sign problem throughout the extended parameter space from the Shastry-Sutherland to the fully frustrated bilayer model and compare it with the phase diagram computed by tensor-network methods. We use QMC to compute with high accuracy the temperature dependence of the magnetic specific heat and susceptibility of the Shastry-Sutherland model for large systems up to a coupling ratio of 0.526(1) and down to zero temperature. For larger coupling ratios, our QMC results assist us in benchmarking the evolution of the thermodynamic properties by systematic comparison with exact diagonalization calculations and interpolated high-temperature series expansions. arXiv:1808.02043v2 [cond-mat.str-el] FIG. 1. Schematic representations of the extended Shastry-Sutherland model [Eq. (2)] in (a) single-plane and (b) bilayer format.

Infinite projected entangled pair states simulations of the S = 1 bilinear-biquadratic Heisenberg model on the square lattice reveal an emergent Haldane phase in between the previously predicted antiferromagnetic and 3-sublattice 120 • magnetically ordered phases. This intermediate phase preserves SU(2) spin and translational symmetry but breaks lattice rotational symmetry, and it can be adiabatically connected to the Haldane phase of decoupled S = 1 chains. Our results contradict previous studies which found a direct transition between the two magnetically ordered states.The search for novel states of matter in quantum manybody systems is one of the most active areas in condensed matter physics. A fascinating example is the ground state of the S = 1 antiferromagnetic Heisenberg chain which, unlike the S = 1/2 chain, exhibits an energy gap, exponentially decaying spin-spin correlations, and gapless edge excitations in case of open boundaries. Thanks to Haldane's pioneering work and conjecture that such a gapped state emerges in integer Heisenberg spin chains in general [1,2], this phase has been named after him.The Haldane phase also extends to related S = 1 models, such as weakly-coupled S = 1 Heisenberg chains [3][4][5][6][7] which are realized in several quasi-1D materials [8][9][10][11][12][13], or the S = 1 bilinear-biquadratic Heisenberg (BBH) chain with Hamiltonian H = i,j cos(θ)S i · S j + sin(θ) (S i · S j ) 2 , for θ in between −π/4 and π/4. More recently, the Haldane phase has been understood as a simple example of a symmetry protected topological (SPT) phase [14][15][16][17].In the present work we focus on the BBH model in two dimensions, which has gained much interest in recent years [18][19][20][21][22][23][24][25][26]; firstly, due to its possible connection to the triangular lattice compounds NiGa 2 S 4 [27] and Ba 3 NiSb 2 O 9 [25, 28-30], and secondly, for θ = π/4, the model is equivalent to the SU(3) Heisenberg model which can be experimentally realized using ultra-cold fermionic atoms in optical lattices [31][32][33][34]. The latter has been shown to exhibit 3-sublattice order on the square and triangular lattices [35,36], and an important question concerns the stability of this phase away from the SU(3) symmetric point. Previous studies on the square lattice based on linear flavor-wave theory [24], exact diagonalization [24], and series expansion [26] predicted a direct transition between the AF and the 3-sublattice phase for θ ≈ 0.2π. However, the accurate study of this parameter regime remains very challenging because Quantum Monte Carlo suffers from the negative sign problem.In this paper we show, using state-of-the-art tensor network simulations, that in between the AF and the 3- AF phaseHaldane phase 3-SL 120° phase 0.217(4) 0.189 (2) FIG. 1. Haldane phase emerging in between the antiferromagnetic (AF) and the 3-sublattice 120 • ordered phases.sublattice phase an intermediate quantum paramagnetic phase emerges which preserves translational and SU(2) spin symmetry, but breaks lattice rota...