toolbox/makekra

Introduction

Once the analytical continuation is finished, we can obtain the spectral function $A(\omega)$ and the imaginary part of the real-frequency Green's function $\Im G(\omega)$,

$$A(\omega) = -\frac{\Im G(\omega)}{\pi}$$

From the well-known Kramers-Kronig transformation, the real part of $G(\omega)$ can be determined as well:

$$\Re G(\omega) = -\frac{1}{\pi} \int^{\infty}_{-\infty} d\omega' \frac{\Im G(\omega)}{\omega - \omega'}$$

In the HIBISCUS component, we offer a Fortran code to do this job. This is the toolbox/makekra code.

The makekra code reads the density of states data, and then calculate the imaginary part of Matsubara green's function. And then using the Kramers-Kronig transformation, we can calculate the real part of the Matsubara green's function easily. So the complete green's function is obtained, which can be used to calculate the self-energy function on real axis by the invert Hilbert transformation.

Usage

$ ./mkra

Input

• See the terminal prompt
• mem.dos.dat (necessary)

Output

• kra.grn.dat

Comment

Now this code is interfaced with HIBISCUS/entropy code merely. It can read the mem.dos.dat file as input data. While to interface it with the HIBISCUS/stoch code is very simple. What you need to do is to rename sac.imsum.dat to mem.dos.dat file, and then supplement the data for different orbitals.