A real-space Green’s function approach for disordered Hubbard model

Towfiq Ahmed, Joshua J. Kas, John J. Rehr

Fabio Siringo

— The real-space single-particle Green’s function formalism is extended to the attractive disordered Hubbard Hamiltonian by matrix Nambu notation, thus providing a general approach to the superconductive instability of a disordered system in quantum mean-field approximation. Configurational averages may be performed by a recent method, already employed for the repulsive model, thus allowing for spatial fluctuations of the local order parameter. The method is shown to be a natural way of investigating the validity limit of the Anderson theorem. An exact analytical solution is provided for a Bethe lattice with no diagonal disorder and infinitely large connectivity.

Oinam Nganba Meetei, Nandini Trivedi

Wolfgang Weller, Frank Stefani, M. Souleiman

Following a proposal by Aronov and Ioselevich, we express the Green functions (GF) of a noninteracting disordered Fermi system as a functional integral on a real time/frequency lattice. The normalizing denominator of this functional integral is equal to unity, because of identities satisfied by the GF. The GF can then be simply averaged with respect to the random disorder potential. We describe the fermionic fields not belonging to the external frequency by means of a bosonic auxiliary field g. The Hubbard-Stratonovich field Q is introduced only with respect to the fermionic fields for the external frequency.

Andro Sabashvili

This work describes a new formalism for Fermionic thermal Greens functions that are discretized in imaginary time. The discretization makes the thermal Greens function periodic in imaginary (Matsubara) frequency space and requires a generalisation of the Dyson equation and Luttinger-Ward-Baym-Kadanoff functional. A Pade method is used to perform an analytic continuation of the periodized Matsubara Greens function to real frequencies which conserves the spectral weight and thus the discontinuity of the corresponding real time Greens function at t = 0. Due to the Matsubara Greens function periodicity, the discrete imaginary frequency space is relatively small which allows calculations at the extremely high precision which is necessary to perform a reliable Pade fit. We use the method to compute the single particle spectral function and energy loss function for doped bilayer graphene in the two-band limit, described by parabolic dispersion and Coulomb interaction. Calculations are performed in both the random phase approximation (RPA) and the fully self-consistent GW approximation. The formalism is also applied to dynamical mean field the- ory calculations using iterated perturbation theory (IPT) for the paramagnetic Hubbard model.

M. Gulácsi, Kevin S. Bedell