Herbert Fotso

Parquet approximation for the 4x4 Hubbard cluster.

We present a numerical solution of the parquet approximation, a conserving diagrammatic approach which is self-consistent at both the single-particle and the two-particle levels. The fully irreducible vertex is approximated by the bare interaction thus producing the simplest approximation that one can perform with the set of equations involved in the formalism. The method is applied to the Hubbard model on a half-filled 4x4 cluster. Results are compared to those obtained from determinant quantum Monte Carlo (DQMC), FLuctuation EXchange (FLEX), and self-consistent second-order approximation methods. This comparison shows a satisfactory agreement with DQMC and a significant improvement over the FLEX or the self-consistent second-order approximation.

Proximity of the Superconducting Dome and the Quantum Critical Point in the Two-Dimensional Hubbard Model

We use the dynamical cluster approximation to understand the proximity of the superconducting dome to the quantum critical point in the two-dimensional Hubbard model. In a BCS formalism, T(c) may be enhanced through an increase in the d-wave pairing interaction (V(d)) or the bare pairing susceptibility (χ(0d)). At optimal doping, where V(d) is revealed to be featureless, we find a power-law behavior of χ(0d)(ω=0), replacing the BCS log, and strongly enhanced T(c). We suggest experiments to verify our predictions.

Solving the parquet equations for the Hubbard model beyond weak coupling

We find that imposing crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When crossing symmetry is not imposed, the convergence of both simple iteration and more complicated continuous loading (homotopy) methods is limited to high temperatures and weak interactions. We modify the algorithm to impose the crossing symmetry without increasing the computational complexity. We also imposed time reversal and a subset of the point group symmetries, but they did not further improve the convergence. We elaborate the details of the latency hiding scheme which can significantly improve the performance in the computational implementation. With these modifications, stable solutions for the parquet equations can be obtained by iteration more quickly even for values of the interaction that are a significant fraction of the bandwidth and for temperatures that are much smaller than the bandwidth. This may represent a crucial step towards the solution of two-particle field theories for correlated electron models.

Dual fermion dynamical cluster approach for strongly correlated systems

We have designed a multiscale approach for strongly correlated systems by combining the dynamical cluster approximation (DCA) and the recently introduced dual fermion formalism. This approach employs an exact mapping from a real lattice to a DCA cluster of linear size

Thermalization of field driven quantum systems

{L}_{c}

Dynamical Cluster Approximation

embedded in a dual fermion lattice. Short-length-scale physics is addressed by the DCA cluster calculation, while longer-length-scale physics is addressed diagrammatically using dual fermions. The bare and dressed dual fermionic Green functions scale as

Absorption spectrum of a two-level system subjected to a periodic pulse sequence

\mathcal{O}(1/{L}_{c})

Frustrated phase separation in the momentum distribution of field-driven light-heavy Fermi-Fermi mixtures of ultracold atoms

, so perturbation theory on the dual lattice converges very quickly, e.g., the dual Fermion self-energy calculated with simple second-order perturbation theory is of order

Suppressing Spectral Diffusion of Emitted Photons with Optical Pulses.

\mathcal{O}(1/{L}_{c}^{3})

Extended Correlation in Strongly Correlated Systems, Beyond Dynamical Cluster Approximation

with third-order and three-body corrections down by an additional factor of