Year: 2019
Type: article
Abstract: An essential ingredient in many model Hamiltonians, such as the Hubbard model, is the effective electron-electron interaction $U$, which enters as matrix elements in some localized basis. These matrix elements provide the necessary information in the model, but the localized basis is incomplete for describing $U$. We present a systematic scheme for computing the manifestly basis-independent dynamical interaction in position representation, $U(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}};\ensuremath{\omega})$, and its Fourier transform to time domain, $U(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}};\ensuremath{\tau})$. These functions can serve as an unbiased tool for the construction of model Hamiltonians. For illustration we apply the scheme within the constrained random-phase approximation to the cuprate parent compounds ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ and ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}$ within the commonly used one- and three-band models, and to nonsuperconducting ${\mathrm{SrVO}}_{3}$ within the ${t}_{2g}$ model. Our method is used to investigate the shape and strength of screening channels in the compounds. We show that the $\mathrm{O}\phantom{\rule{0.16em}{0ex}}2{p}_{x,y}\ensuremath{-}\mathrm{Cu}\phantom{\rule{0.16em}{0ex}}3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ screening gives rise to regions with strong attractive static interaction in the minimal (one-band) model in both cuprates. On the other hand, in the minimal (${t}_{2g}$) model of ${\mathrm{SrVO}}_{3}$ only regions with a minute attractive interaction are found. The temporal interaction exhibits generic damped oscillations in all compounds, and its time integral is shown to be the potential caused by inserting a frozen point charge at $\ensuremath{\tau}=0$. When studying the latter within the three-band model for the cuprates, short time intervals are found to produce a negative potential.
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Vetenskapsrådet
OpenAlex ID: W2911279926