Electron-electron interactions can induce Fermi surface deformations which break the point-group symmetry of the lattice structure of the system. In the vicinity of such a "Pomeranchuk instability" the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We show that critical Fermi surface fluctuations near a d-wave Pomeranchuk instability in two dimensions lead to large anisotropic decay rates for single-particle excitations, which destroy Fermi liquid behavior over the whole surface except at the Brillouin zone diagonal.

We propose an interaction flow scheme that sums up the perturbation expansion of many-particle systems by successively increasing the interaction strength. It combines the unbiasedness of renormalization group methods with the simplicity of straight-forward perturbation theory. Applying the scheme to fermions in one dimension and to the two-dimensional Hubbard model we find that at one-loop level and low temperatures there is ample agreement with previous one-loop renormalization group approaches. We furthermore present results for the momentum-dependence of spin, charge and pairing interactions in the two-dimensional Hubbard model.Comment: 14 pages, 14 figure

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We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional insertions of truncated partitions of unity. These insertions decouple the fermionic propagators from the exchange propagators and lead to a separation of the underlying equations. We demonstrate that this separation is numerically advantageous and may pave the way for refined, large-scale computational investigations even in the case of complex multiband systems. Furthermore, on the basis of speedup data gained from our implementation, it is shown that this new variant facilitates efficient calculations on a large number of multi-core CPUs. We apply the scheme to the t,t ′ Hubbard model on a square lattice to analyze the convergence of the results with the bond length of the truncation of the partition of unity. In most parameter areas, a fast convergence can be observed. Finally, we compare to previous results in order to relate our approach to other fRG studies.

We analyze the competition between antiferromagnetism and superconductivity in the two-dimensional Hubbard model by combining a functional renormalization group flow with a mean-field theory for spontaneous symmetry breaking. Effective interactions are computed by integrating out states above a scale Λ MF in one-loop approximation, which captures in particular the generation of an attraction in the dwave Cooper channel from fluctuations in the particle-hole channel. These effective interactions are then used as an input for a mean-field treatment of the remaining low-energy states, with antiferromagnetism, singlet superconductivity and triplet πpairing as the possible order parameters. Antiferromagnetism and superconductivity suppress each other, leaving only a small region in parameter space where both orders can coexist with a sizable order parameter for each. Triplet π-pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small.

We analyze the interaction-induced renormalization of single-particle excitations in the two-dimensional Hubbard model at weak coupling using the Wick-ordered version of the functional renormalization group. The self-energy is computed for real frequencies by integrating a flow equation with renormalized two-particle interactions. In the vicinity of hot spots, that is, points where the Fermi surface intersects the umklapp surface, self-energy effects beyond the usual quasiparticle renormalizations and damping occur near instabilities of the normal, metallic phase. Strongly enhanced renormalized interactions between particles at different hot spots generate a pronounced low-energy peak in the imaginary part of the self-energy, leading to a pseudogaplike double-peak structure in the spectral function for single-particle excitations.

One-particle spectral properties in the normal phase of the two-dimensional attractive Hubbard model are investigated in the weak coupling regime using the non-selfconsistent T-matrix approximation. The corresponding equations are evaluated numerically directly on the real frequency axis.For temperatures sufficiently close to the superconducting transition temperature a pseudogap in the one-particle spectral function is observed, which can be assigned to the increasing importance of pair fluctuations.

We compare laser Doppler vibrometry (LDV) and digital image correlation (DIC) for use in full-field vibration and modal testing. This was done using a simultaneously measured 3D displacement field on a flat 7-inch corner-supported metal plate using pseudorandom excitation via a shaker. We complete a detailed comparison between the techniques and discuss the pros and cons of each. The results show that either technique can be used for quantifying the modal information with the LDV providing better out-of-plane displacement resolution and equivalent in-plane resolution. The strain calculation is considered better in the DIC approach due to the direct tie to the surface displacements. While the LDV does not lose its place as the gold standard for modal testing, DIC has introduced a new and competitive approach that will have significant advantages in certain testing regimes.