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 introduce an efficient way to improve the accuracy of projected wave functions, widely used to study the two-dimensional Hubbard model. Taking the clue from the backflow contribution, whose relevance has been emphasized for various interacting systems on the continuum, we consider many-body correlations to construct a suitable approximation for the ground state at intermediate and strong couplings. In particular, we study the phase diagram of the frustrated t − tЈ Hubbard model on the square lattice and show that, thanks to backflow correlations, an insulating and nonmagnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio tЈ / t.

The two-dimensional Hubbard model on the anisotropic triangular lattice, with two different hopping amplitudes t and t ′ , is relevant to describe the low-energy physics of κ-(ET)2X, a family of organic salts. The ground-state properties of this model are studied by using Monte Carlo techniques, on the basis of a recent definition of backflow correlations for strongly-correlated lattice systems. The results show that there is no magnetic order for reasonably large values of the electron-electron interaction U and frustrating ratio t ′ /t = 0.85, suitable to describe the non-magnetic compound with X=Cu2(CN)3. On the contrary, Néel order takes place for weaker frustrations, i.e., t ′ /t ∼ 0.4 ÷ 0.6, suitable for materials with X=Cu2(SCN)2, Cu[N(CN)2]Cl, or Cu[N(CN)2]Br.

By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional HubbardHolstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping t, the on-site electron-electron interaction U , the phonon energy ω0, and the electron-phonon coupling g. At half filling, the ground state is an antiferromagnetic insulator for U 2g 2 /ω0, while it is a charge-density-wave (or bi-polaronic) insulator for U 2g 2 /ω0. In addition to these phases, we find a superconducting phase that intrudes between them. For ω0/t = 1, superconductivity emerges when both U/t and 2g 2 /tω0 are small; then, by increasing the value of the phonon energy ω0, it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case.