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

We suggest that a randomization of the pseudo-dipolar interaction in the spin-orbit-generated lowenergy Hamiltonian of YbMgGaO4 due to an inhomogeneous charge environment from a natural mixing of Mg 2+ and Ga 3+ can give rise to orientational spin disorder and mimic a spin-liquid-like state. In the absence of such quenched disorder, 1/S and density matrix renormalization group calculations both show robust ordered states for the physically relevant phases of the model. Our scenario is consistent with the available experimental data and further experiments are proposed to support it.PACS numbers: 75.10. Jm, 75.40.Gb, 78.70.Nx Dating back to Wannier's pioneering study of the Ising model [1], triangular lattice models and materials with frustrating antiferromagnetic interactions have served as fertile playgrounds for new ideas [2][3][4][5][6][7][8][9][10]. These systems continue to draw significant experimental [11][12][13][14][15] and theoretical interest because they exhibit many intriguing novel ordered states [16][17][18][19][20][21][22] and unusual continuumlike spectral features [23][24][25][26][27][28][29][30][31] and especially because they provide a setting for spin-liquid states [32][33][34][35][36][37][38][39][40][41][42].Among the latest experimental discoveries [14,15], a rare-earth triangular-lattice antiferromagnet YbMgGaO 4 has recently emerged as a new candidate for a quantum spin liquid of the effective spin-1/2 degrees of freedom of Yb 3+ ions [43,44]. It has been argued that the spin-orbit origin of its magnetic properties and the pseudo-spin nature of the low-energy states with highly anisotropic effective spin interactions may potentially open a new route to realizing quantum spin liquids [44][45][46]. While the lack of ordering, anomalous specific heat, and especially continuum-like excitations in inelastic neutron scattering [45,47] all provide strong support to the idea of an intrinsic spin liquid, other experimental findings are increasingly at odds with this picture.First, in magnetization vs field measurements, there is no sharpening of the transition to the saturated phase upon lowering the temperature, and the lack of the upward curvature in M (H) at the lowest T 's [43,44] is indicative of low quantum fluctuations in the ground state [48]. Second, in the high-field polarized phase, neutron scattering shows that continuum-like excitations persist, with significant smearing of magnon lines that are expected to be sharp [47]. In addition, an apparent absence of any detectable contribution of spin excitations to thermal conductivity down to the lowest temperatures, accompanied by a strong deviation of the phonon part from the ballistic T 3 form [49], both suggest strong scattering effects. These, combined with the anomalously broadened higher-energy Yb 3+ doublet structure [47, 50] and a ubiquitous mixing of Mg 2+ and Ga 3+ ions in the non-magnetic layers [43,47], implicate disorder as a key contributor to the observed properties [50].In this Letter, we first argue that a hypothetical,...

Using the density matrix renormalization group, we investigate the S = 1/2 Heisenberg model on the honeycomb lattice with first (J(1)) and second (J(2)) neighbor interactions. We are able to study long open cylinders with widths up to 12 lattice spacings. For J(2)/J(1) near 0.3, we find an apparently paramagnetic phase, bordered by an antiferromagnetic phase for J(2) ≲ 0.26 and by a valence bond crystal for J(2) ≳ 0.36. The longest correlation length that we find in this intermediate phase is for plaquette valence bond order. This correlation length grows strongly with cylinder circumference, indicating either quantum criticality or weak plaquette valence bond order.

No abstract

Spin systems with frustrated anisotropic interactions are of significant interest due to possible exotic ground states. We have explored their phase diagram on a nearest-neighbor triangular lattice using the density-matrix renormalization group and mapped out the topography of the region that can harbor a spin liquid. We find that this spin-liquid phase is continuously connected to a previously discovered spin-liquid phase of the isotropic J_{1}-J_{2} model. The two limits show nearly identical spin correlations, making the case that their respective spin liquids are isomorphic to each other.