Accelerating GW in 2D systems

From The Yambo Project
Jump to navigation Jump to search

Since Yambo v5.1 it is possible to use an algorithm able to accelerate convergences of GW calculations in two-dimensional systems with respect to the k point sampling.

The method is explained in the paper:

Efficient GW calculations in two-dimensional materials through a stochastic integration of the screened potential

A. Guandalini, P. D'Amico, A. Ferretti and D. Varsano

available at the link: https://arxiv.org/abs/2205.11946

The method makes use of a truncated Coulomb potential in a slab geometry that in Fourier space reads:

[math]\displaystyle{ V_G(q)=\frac{4\pi}{\vert q+G \vert^2}[1-e^{-\vert q_\parallel+G_\parallel\vert L/2}cos[(q_z+G_z)L/2)] }[/math]

where L is the length of the cell in the non-periodic z direction. As the q-grid is 2D, we have [math]\displaystyle{ q_z = 0. }[/math]

To activate the algorithm it is needed to add the RIM_W in your GW input file:

Convergence of the quasiparticle band gap of MoS2 , hBN (and phosphorene with respect to the number of sampling points of the BZ. Blue lines indicate results obtained with standard integration methods. The extrapolated values are indicated with an horizontal dashed line. Orange lines are the results obtained with the W-av method. The grey shaded regions show the converge tolerance (±50 meV) and are centered at the extrapolated values.
rim_cut                          # [R] Coulomb potential
HF_and_locXC                     # [R] Hartree-Fock
gw0                              # [R] GW approximation
ppa                              # [R][Xp] Plasmon Pole Approximation for the Screened Interaction
dyson                            # [R] Dyson Equation solver
em1d                             # [R][X] Dynamically Screened Interaction
RIM_W                            # Activate the RIM_W algorithm

and set the "slab z" Coulomb cutoff:

CUTGeo= "slab z"                   # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere/ws/slab X/Y/Z/XY..

where z is the non periodic direction.

and finally define the variable governing the Monte Carlo integration e.g.:

RandQpts=3000000                  # [RIM] Number of random q-points in the BZ
RandGvec= 97                RL    # [RIM] Coulomb interaction RS components
RandGvecW = 15              RL

here RandGvecW defines the number of G vectors to integrate W outside the BZ.


Links