Screening of Long-Range Coulomb Interactions in Hubbard Electron Systems

Anonymous

Connie H. Mousatov, Ilya Esterlis, Sean A. Hartnoll

Priyanka Aggarwal, Ram Kuntal Hazra, Bharti Kapil +2 more

The calculation of the many-electron (screened) Coulomb and exchange integrals is a very common task to perform in modern electronic structure theory. While an analytical treatment of the complete integrals is too complicated to be attempted directly, essential insight can be gained by focusing on the most significant contributions, as determined by a physical criterion. The monopole term of the screened Coulomb interaction is particularly important, since it defines the Hubbard interaction U among a set of localized electrons, which is an essential parameter for effective models of strongly correlated systems. Here, we derive an analytical solution for the matrix elements of the screened Coulomb interaction on a plane-wave basis, which is routinely used in the most common methods for electronic structure calculations. Screening is treated using a Yukawa potential, which is suitable to describe the valence electrons in the Fermi level region. For the solution of the integrals, the plane waves and the Yukawa potential are first expanded in Bessel functions of first and second kind. Then, by means of the lower and upper incomplete gamma functions, we are able to obtain closed-form integrals of a series that remains convergent for realistic parameters. Our exact solution for the radial integrals of the monopole term can find usage in plane-wave codes for electronic structure calculations, both as an output tool as well as within the computational cycle, as e.g., for many-body extensions of density-functional theory. Considering the importance of Bessel functions in solid state physics and electronic structure theory, it is also easy to foresee that our solution to the various integrals across this work may become useful to several other problems in the field. • Analytical method for matrix elements of the screened Coulomb interaction in plane wave. • Analysis of the monopole term, significant as the Hubbard U in strongly correlated systems. • Closed-form solutions achieved for both long-range and short-range components of integrals. • Method generalizable to evaluate higher-order terms. • Anticipated applicability to plane-wave codes for physical analysis and hybrid functional routines.

J. P. Hague, P. E. Kornilovitch

We present details of a continuous-time quantum Monte Carlo algorithm for the screened Hubbard-Fr\"ohlich bipolaron. We simulate the bipolaron in one dimension with arbitrary interaction range in the presence of Coulomb repulsion, computing the effective mass, binding energy, total number of phonons associated with the bipolaron, mass isotope exponent, and bipolaron radius in a comprehensive survey of the parameter space. We discuss the role of the range of the electron-phonon interaction, demonstrating the evolution from Holstein to Fr\"ohlich bipolarons and we compare the properties of bipolarons with singlet and triplet pairing. Finally, we present simulations of the bipolaron dispersion. The bandwidth of the Fr\"ohlich bipolaron is found to be broad and the decrease in bandwidth as the two polarons bind into a bipolaron is found to be far less rapid than in the case of the Holstein interaction. The properties of bipolarons formed from long-range electron-phonon interactions, such as light strongly bound bipolarons and intersite pairing when Coulomb repulsion is large, are found to be robust against screening, with qualitative differences between Holstein and screened Fr\"ohlich bipolarons found even for interactions screened within a single lattice site.

H.-B. Schüttler, Gökhan Esirgen, N. E. Bickers

Ho-Kin Tang, Indra Yudhistira, Udvas Chattopadhyay +4 more

The absence of screening of the nonlocal Coulomb interaction in Dirac systems at charge neutrality leads to the breakdown of the Fermi liquid and divergence of the Fermi velocity. On the other hand, Mott-Hubbard physics and the concomitant formation of local moments is dominated by the local effective Hubbard interaction. Using quantum Monte Carlo methods combined with stochastic analytical continuation, we compute the single particle spectral function of fermions on the honeycomb lattice for a realistic interaction that includes both the Hubbard interaction and long-ranged Coulomb repulsion. To a first approximation, we find that the generic high-energy features, such as the formation of the upper Hubbard band near the phase transition, are primarily determined by the local effective Hubbard interaction. In the weakly interacting regime, the long-range Coulomb interaction enhances the bandwidth of quasiparticles and suppresses their lifetime. Conversely, near the phase transition, the long-range Coulomb interaction suppresses the background antiferromagnetic fluctuation, which potentially promotes the propagation of spin polarons, leading to a slight enhancement of the quasiparticle spectral weight and lifetime.