Real-space Green's Function Calculations including Hubbard Contributions

Liu Yang, Yao Ma

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.

BoGyu Jang

B. D. E. McNiven, G. Todd Andrews, J. P. F. LeBlanc

We generate the perturbative expansion of the single particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle quantities for real and Matsubara frequencies and verify results through comparison to existing data on the Matsubara axis. With low-order expansions at weak coupling we observe a number of outcomes expected at higher orders: the opening of a gap, pseudogap behavior, and Fermi-surface reconstruction. Based on low-order perturbations, we consider the phase diagram that arises from truncated expansions of the self-energy and Green's function and their relation via the Dyson equation. From Matsubara axis data, we observe insulating behavior in direct expansions of the Green's function, whereas the same order of truncation of the self-energy produces metallic behavior. This observation is supported by additional calculations for real frequencies. We attribute this difference to the order in which diagrams are implicitly summed in the Dyson series. By separating the reducible and irreducible contributions at each order we show that the reducible diagrams implicitly summed in the Dyson equation lead to incorrect physics in the half-filled Hubbard model. Our observations for this particular case lead us to question the utility of the Dyson equation for any problem that shows a disparity between reducible and irreducible contributions to the expansion of the Green's function.

Oracio Navarro, E. Flores, M. Avignon

Francesco Libbi, Jacopo Rizzo, Francesco Tacchino +2 more

We propose an improved quantum algorithm to calculate the Green's function through real-time propagation, and use it to compute the retarded Green's function for the two-, three-, and four-site Hubbard models. This protocol significantly reduces the number of controlled operations when compared to those previously suggested in literature. Such reduction is quite remarkable when considering the two-site Hubbard model, for which we show that it is possible to obtain the exact time propagation of the $|N\ifmmode\pm\else\textpm\fi{}1\ensuremath{\rangle}$ states by exponentiating one single Pauli component of the Hamiltonian, allowing us to perform the calculations on an actual superconducting quantum processor.