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(r,r′;ω), and its Fourier transform to time domain, U(r,r′;τ). 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 La2CuO4 and HgBa2CuO4 within the commonly used one- and three-band models, and to nonsuperconducting SrVO3 within the t2g model. Our method is used to investigate the shape and strength of screening channels in the compounds. We show that the O2px,y-Cu3dx2-y2 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 (t2g) model of SrVO3 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 τ=0. When studying the latter within the three-band model for the cuprates, short time intervals are found to produce a negative potential.
Subject classification (UKÄ)
- Condensed Matter Physics