Overview

In this document, we introduce how we compute downfolded models with mVMC or ${\mathcal H}\Phi$ in conjunction to RESPACK.

$$\begin{split}\begin{aligned} {\cal H} &= \sum_{i, j, \alpha, \beta, \sigma} t_{i \alpha j \beta} c_{i \alpha \sigma}^{\dagger} c_{j \beta \sigma} \nonumber \\ &+ \sum_{i, \alpha} U_{i \alpha i \alpha} n_{i \alpha \uparrow} n_{j \alpha \downarrow} + \sum_{(i, \alpha) \lt (j, \beta)} U_{i \alpha j \beta} n_{i \alpha} n_{j \beta} - \sum_{(i, \alpha) \lt (j, \beta)} J_{i \alpha j \beta} (n_{i \alpha \uparrow} n_{j \beta \uparrow} + n_{i \alpha \downarrow} n_{j \beta \downarrow}) \nonumber \\ &+ \sum_{(i, \alpha) \lt (j, \beta)} J_{i \alpha j \beta} ( c_{i \alpha \uparrow}^{\dagger} c_{j \beta \downarrow}^{\dagger} c_{i \alpha \downarrow} c_{j \beta \uparrow} + c_{j \beta \uparrow}^{\dagger} c_{i \alpha \downarrow}^{\dagger} c_{j \beta \downarrow} c_{j \alpha \uparrow} ) \nonumber \\ &+ \sum_{(i, \alpha) \lt (j, \beta)} J_{i \alpha j \beta} ( c_{i \alpha \uparrow}^{\dagger} c_{i \alpha \downarrow}^{\dagger} c_{j \beta \downarrow} c_{j \beta \uparrow} + c_{j \beta \uparrow}^{\dagger} c_{j \beta \downarrow}^{\dagger} c_{i \alpha \downarrow} c_{i \alpha \uparrow} ) \end{aligned}\end{split}$$

Prerequisite

We compute the Kohn-Sham orbitals with QuantumESPRESSO or xTAPP, and obtain the Wannier function, the dielectric function, the effective interaction with RESPACK, and simulate quantum lattice models with mVMC or ${\mathcal H}\Phi$. Therefore, these programs must be available in our machine.