Role of charge and spin fluctuations and their interplay in solids : A Green’s function approach

Abstract: Due to the large number of electrons, solid state physics boils down to many-body approximations in which only selected types of collective excitations are taken into account, guided by the emergent properties of the material under study. In this thesis, the collective excitations of primary interest are electronic charge and spin fluctuations(plasmons and magnons) and nuclear charge fluctuations (phonons). Part I introduces the many-electron problem and provides a background theory for charge and spin fluctuations. Part II introduces the papers andsummarizes their key results. These are appended in their published form in Part III.In Paper I, electronic charge fluctuation effects are studied within the random-phase approximation through the spatiotemporal behavior of Hedin’s screened interaction W (and the partially screened analog U) in two cuprates (La2CuO4 and HgBa2CuO4) and in SrVO3, from initial local density calculations. The 1- and 3-band models for the cuprates produce, respectively, stable and short-lived regions with a negative effective interaction U. In Paper II, the effect of electronic charge fluctuations on the orbital magnetization is studied in the spin-1/2 Haldane-Hubbard model by computing it using the one-shot GW Green’s function. The major finding is that,for a small local repulsion, interband charge fluctuations boost the orbital magnetization if the inversion symmetry breaking staggered potential is larger than the nearest-neighbor hopping.In Paper III, which comprises the major work of this thesis, a microscopic Green’s function formula for the exchange-mediated contribution to the magnon-phonon interaction is derived from the underlying electronic structure. Despite the absence of spin-orbit induced magnon-phonon interconversion, the room-temperaturerenormalized magnon spectra acquire splittings due to phonon absorption in a minimal three-dimensional model.In Paper IV, a new formalism for the Green’s function, which relies on neither self-energy nor Dyson’s equation and is based on a time delay-extended exchange-correlation potential Vxc, is applied to the half-filled1-band Hubbard chain. Vxc is approximated by that of the Hubbard dimer, which is accessible analytically. The one-shot analytic spectra agree well with the density-matrix renormalization group method, and the U-dependent band gap is very close to the exact solution.