Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods. arXiv:1505.02290v2 [cond-mat.str-el] 15

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We report the observation of magnetic superstructure in a magnetization plateau state of SrCu 2 (BO 3 ) 2 , a frustrated quasi-two-dimensional quantum spin system. The Cu and B nuclear magnetic resonance (NMR) spectra at 35 millikelvin indicate an apparently discontinuous phase transition from uniform magnetization to a modulated superstructure near 27 tesla, above which a magnetization plateau at 1/8 of the full saturation has been observed. Comparison of the Cu NMR spectrum and the theoretical analysis of a Heisenberg spin model demonstrates the crystallization of itinerant triplets in the plateau phase within a large rhomboid unit cell (16 spins per layer) showing oscillations of the spin polarization. Thus we are now in possession of an interesting model system to study a localization transition of strongly interacting quantum particles.Published in Science 298, 395 (2002).

We study the energy and the static spin structure factor of the ground state of the spin-1/2 quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) U (1) Dirac spin liquid is competitive with previously proposed gapped (topological) Z2 spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site E/J = −0.4365(2), which is equal, within three error bars, to the estimates given by the density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant system, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite toric clusters at the pure variational level, our energies are lower compared to those from DMRG calculations.PACS numbers: 75.10. Jm, 75.10.Kt, 75.40.Mg, 75.50.Ee Introduction. The spin-1/2 quantum Heisenberg antiferromagnet (QHAF) on the kagome lattice provides a conducive environment to stabilize a quantum paramagnetic phase of matter down to zero temperature, [1][2][3] a fact that has been convincingly established theoretically from several studies, including exact diagonalization, 4-8 series expansion, 9,10 quantum Monte Carlo, 11and analytical techniques. 12 The question of the precise nature of the spin-liquid state of the kagome spin-1/2 QHAF has been intensely debated on the theoretical front, albeit without any definitive conclusions. Different approximate numerical techniques have claimed a variety of ground states. On the one hand, densitymatrix renormalization group (DMRG) calculations have been claimed for a fully gapped (nonchiral) Z 2 topological spin-liquid ground state that does not break any point group symmetry.13,14 On the other hand, an algebraic and fully symmetric U (1) Dirac spin liquid has been proposed as the ground state, by using projected fermionic wave functions and the variational Monte Carlo (VMC) approach. [15][16][17][18][19][20] In addition, valence bond crystals have been suggested from many other techniques. In particular, a 36-site unit cell valence-bond crystal [21][22][23] was proposed using quantum dimer models, 24-28 series expansion 29,30 and multiscale entanglement renormalization ansatz (MERA) 31 techniques. Finally, a recent coupled cluster method (CCM) suggested a q = 0 (uniform) state. 32On general theoretical grounds, the Z 2 spin liquids in two spatial dimensions are known to be stable phases, 33-35 as compared to algebraic U (1) spin liquids, which are known to be only marginally stable.36 However, explicit numerical calculations using projected wave functions have shown the U (1) Dirac spin liquid to be stable (locally and globally) with respect to dimerizing into all known valence-bond crystal phases. 15,17,18,20 Furthermore, it was shown that, within this class of Gutzwiller projected wave functions, all the fully symmetric, gapped Z 2 spin ...