Green's Functions for Quantum Fermi Systems of Charged Colliding Particles

N.U. Nazarov, О. А. Пономарев

M. Ya. Amus’ya

V. N. Melnikov

Jacopo Rizzo, Francesco Libbi, Francesco Tacchino +3 more

Many-body Green's functions encode all the properties and excitations of interacting electrons. While these are challenging to be evaluated accurately on a classical computer, recent efforts have been directed toward finding quantum algorithms that may provide a quantum advantage for this task, exploiting architectures that will become available in the near future. In this work we introduce a novel near-term quantum algorithm for computing one-particle Green's functions via their Lehmann representation. The method is based on a generalization of the quantum equation of motion algorithm that gives access to the charged excitations of the system. We demonstrate the validity of the present proposal by computing the Green's function of a two-site Fermi-Hubbard model on a IBM quantum processor.

M. G. Zacher, Enrico Arrigoni, Werner R. Hanke +1 more

The problem of spin-charge separation is analyzed numerically in the metallic phase of the one-band Hubbard model in one dimension by studying the behavior of the single-particle Green's function and of the spin and charge susceptibilities. We first analyze the quantum Monte Carlo data for the imaginary-time Green's function within the maximum-entropy method in order to obtain the spectral function at real frequencies. For some values of the momentum sufficiently away from the Fermi surface two separate peaks are found, which can be identified as charge and spin excitations. In order to improve our accuracy and to be able to extend our study to a larger portion of the Brillouin zone, we also fit our data with the imaginary-time Green's function obtained from the Luttinger-model solution with two different velocities as fitting parameters. The excitation energies associated with these velocities turn out to agree, in a broad range of momenta, with the ones calculated from the charge and spin susceptibilities. This allows us to identify these single-particle excitations as due to a separation of spin and charge. Remarkably, the range of momenta where spin-charge separation is seen extends well beyond the region of linear dispersion about the Fermi surface. We finally discuss a possible extension of our method to detect spin-charge separation numerically in two dimensions.

Donald H. Kobe