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In a recent preprint [arXiv:1803.04118v2] Chern and Barros report numerical simulations of the mean-field interaction quench dynamics, $U_ito U_f$, of the attractive Hubbard model that confirm our earlier prediction [Europhys. Lett. 85, 20004 (2008), arXiv:0805.2798] of spontaneous eruption of spatial inhomogeneities in the post-quench state with periodically oscillating superconducting order. Chern and Barros attribute this instability with respect to spatial fluctuations to the large magnitude of the final Hubbard coupling $U_f$. We point out that this interpretation is inaccurate and discuss further work necessary to numerically verify the mechanism of the instability and the nature of the steady state.
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We study the effect of U=0 impurities on the superconducting and thermodynamic properties of the attractive Hubbard model on a square lattice. Removal of the interaction on a critical fraction of $f_{rm crit} approx 0.30$ of the sites results in the destruction of off-diagonal long range order in the ground state. This critical fraction is roughly independent of filling in the range $0.75 < rho < 1.00$, although our data suggest that $f_{rm crit}$ might be somewhat larger below half-filling than at $rho=1$. We also find that the two peak structure in the specific heat is present at $f$ both below and above the value which destroys long range pairing order. It is expected that the high $T$ peak associated with local pair formation should be robust, but apparently local pairing fluctuations are sufficient to generate a low temperature peak.
We present a study of the attractive Hubbard model based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG). For this study the NRG method is extended to deal with self-consistent solutions of effective impurity models with superconducting symmetry breaking. We give details of this extension and validate our calculations with DMFT results with antiferromagnetic ordering. We also present results for static and integrated quantities for different filling factors in the crossover from weak (BCS) to strong coupling (BEC) superfluidity. We study the evolution of the single-particle spectra throughout the crossover regime. Although the DMFT does not include the interaction of the fermions with the Goldstone mode, we find strong deviations from the mean-field theory in the intermediate and strong coupling (BEC) regimes. In particular, we show that low-energy charge fluctuations induce a transfer of spectral weight from the Bogoliubov quasiparticles to a higher-energy incoherent hump.
We provide a new perspective on the pseudogap physics for attractive fermions as described by the three-dimensional Hubbard model. The pseudogap in the single-particle spectral function, which occurs for temperatures above the critical temperature $T_c$ of the superfluid transition, is often interpreted in terms of preformed, uncondensed pairs. Here we show that the occurrence of pseudogap physics can be consistently understood in terms of local excitations which lead to a splitting of the quasiparticle peak for sufficiently large interaction. This effect becomes prominent at intermediate and high temperatures when the quantum mechanical hopping is incoherent. We clarify the existence of a conjectured temperature below which pseudogap physics is expected to occur. Our results are based on approximating the physics of the three-dimensional Hubbard model by dynamical mean field theory calculations and a momentum independent self-energy. Our predictions can be tested with ultracold atoms in optical lattices with currently available temperatures and spectroscopic techniques.
We study a two-component Fermi system with attractive interactions and different populations of the two species in a cubic lattice. For an intermediate coupling we find a uniformly polarized superfluid which is stable down to very low temperatures. The momentum distribution of this phase closely resembles that of the Sarma phase, characterized by two Fermi surfaces. This phase is shown to be stabilized by a potential energy gain, as in a BCS superfluid, in contrast to the unpolarized BEC which is stabilized by kinetic energy. We present general arguments suggesting that preformed pairs in the unpolarized superfluid favor the stabilization of a polarized superfluid phase.
By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the extended attractive Hubbard model (EAHM) exhibits rich ground state phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders. We study the competition between these superconducting pairing symmetries invoking an unrestricted Hartree-Fock- Bogoliubov-de Gennes (HFBdG) mean-field approach, and we use the d-vector formalism to characterize the nature of the stabilized superconducting orders. We discover that, while all other types of orders are suppressed, a non-unitary triplet order dominates the phase space in the presence of an in-plane external magnetic field. We also find a transition between a non-unitary to unitary superconducting phase driven by the change in average electron density. Our results serve as a reference for identifying and understanding the nature of superconductivity based on the symmetries of the pairing correlations. The results further highlight that EAHM is a suitable effective model for describing most of the pairing symmetries discovered in different materials.
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