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

Kelvin waves (kelvons)-the distortion waves on vortex lines-play a key part in the relaxation of superfluid turbulence at low temperatures. We present a weak-turbulence theory of kelvons. We show that non-trivial kinetics arises only beyond the local-induction approximation and is governed by three-kelvon collisions; corresponding kinetic equation is derived. On the basis of the kinetic equation, we prove the existence of Kolmogorov cascade and find its spectrum. The qualitative analysis is corroborated by numeric study of the kinetic equation. The application of the results to the theory of superfluid turbulence is discussed.PACS numbers: 67.40. Vs, 03.75.Lm, 47.32.Cc The distortion waves on a vortex filament-Kelvin waves (KW)-have been known for more than a century [1]. Superfluids with their topological (quantized) vorticity form a natural domain for KW [2]. Nowadays there is a strong interest to the non-linear aspects of KW associated with studying low-temperature superfluid turbulence of 4 He [3,4,5,6,7,8,9,10], as well as vortex dynamics in ultra-cold atomic gases [11,12].The superfluid turbulence [2, 13] is a chaotic tangle of vortex lines. In the absence of the normal component (T → 0 limit), KW play a crucial part in the vortex tangle relaxational dynamics. In contrast to a normal fluid, the quantization of the velocity circulation in a superfluid makes it impossible for the vortex line to relax by gradually slowing down. The only allowed way of relaxation is reducing the total line length. At T = 0 even this generic scenario becomes non-trivial, as the total line length is, to a very good approximation, a constant of motion. In the scenario proposed by one of us [3], the vortex line length-in the form of KW generated in the process of vortex line reconnections-cascades from the main length scale (typical interline separation, R 0 ) to essentially lower length scales; ultimately decaying into phonons, as it was pointed out by Vinen [4,8].A very specific feature of KW cascade is that the intrinsic vortex line dynamics in the local-induction approximation (LIA) (for an introduction, see, e.g., [2,13]) controlled by the small parameter 1/ ln(R 0 /ξ), with ξ the vortex core radius, is subject to a specific curvatureconservation constraint rendering it unable to support the cascade process [3] (see also below). Within LIA, an "external" ingredient of the vortex line dynamics-the vortex line crossings with subsequent reconnections-is required to push the KW cascade down towards arbitrarily small wavelengths. The most characteristic feature of this LIA scenario, distinguishing it from typical non-linear cascades, is the fragmentation of the vortex lines due to local self-crossings [3]; we will thus refer to this scenario as fragmentational scenario.Experimentally, the main consequence of the existence of a cascade regime, no matter what is its microscopic nature, is independence of the relaxation time of superfluid turbulence on temperature in the T → 0 limit. Davis A general question arises, however, of ho...

Precise understanding of strongly interacting fermions, from electrons in modern materials to nuclear matter, presents a major goal in modern physics. However, the theoretical description of interacting Fermi systems is usually plagued by the intricate quantum statistics at play. Here we present a cross-validation between a new theoretical approach, Bold Diagrammatic Monte Carlo (BDMC), and precision experiments on ultra-cold atoms. Specifically, we compute and measure with unprecedented accuracy the normal-state equation of state of the unitary gas, a prototypical example of a strongly correlated fermionic system. Excellent agreement demonstrates that a series of Feynman diagrams can be controllably resummed in a non-perturbative regime using BDMC. This opens the door to the solution of some of the most challenging problems across many areas of physics.