View source for Real time Bethe-Salpeter Equation (TDSE)

This tutorial will show how to perform a simple real-time BSE calculation with Yambo on hBN monolayer. Use the same DFT inputs of the [http://www.yambo-code.org/educational/tutorials/files/hBN-2D.tar.gz previous tutorial], but increase the number of k-points to <code>10 10 1</code> in such a way to have converged exciton. Follow the first 6 steps of the [[Real time approach to linear response using TDSE|Real time approach to linear response using TDSE]]. Then generate the input file to calculate the collisions (see appendix of [https://arxiv.org/abs/1109.2424 Phys. Rev. B 84, 245110]) use the command : <code> yambo_nl -b -e -v h+sex</code>. The flag -b will tell the code to calculate the dielectric constant that is required for the screened interaction.

 em1s                           # [R Xs] Static Inverse Dielectric Matrix
 collisions                     # [R] Eval the extended Collisions
 dipoles                        # [R   ] Compute the dipoles
 DIP_Threads=0                  # [OPENMP/X] Number of threads for dipoles
 X_Threads=0                    # [OPENMP/X] Number of threads for response functions
 RT_Threads=0                   # [OPENMP/RT] Number of threads for real-time
 Chimod= "HARTREE"              # [X] IP/Hartree/ALDA/LRC/PF/BSfxc
 % BndsRnXs
    1 |  40 |                   # [Xs] Polarization function bands
 %
 NGsBlkXs= <span style="color:red">1000</span> mHa      # [Xs] Response block size
 % DmRngeXs
   0.10000 |  0.10000 | eV      # [Xs] Damping range
 %
 % LongDrXs
  1.000000 | 0.000000 | 0.000000 |        # [Xs] [cc] Electric Field
 %
 % COLLBands
   <span style="color:red">4 |  5 |  </span>                 # [COLL] Bands for the collisions
 %
 HXC_Potential= "HARTREE+SEX"           # [SC] SC HXC Potential
 HARRLvcs= <span style="color:red">1000 </span> mHa      # [HA] Hartree     RL components
 EXXRLvcs= <span style="color:red">1000 </span>mHa      # [XX] Exchange    RL components
 CORRLvcs= <span style="color:red">1000 </span> mHa      # [GW] Correlation RL components
 

With this input, we calculate the HARTREE and SEX collisions integrals. Notice that the HARTREE term in principle can be calculated on the fly, but in this way it is more efficient especially for the non-linear response. Here one has to converge the cutoff for the Hartree and the Screened Exchange, usually 5000 mHa it is a good value, in this example, I put 1000 mHa to speed up calculations. The collisions bands COLLBands have to be the same number of bands you want to use in the linear/nonlinear response. Run this calculation, it will take 5 minutes on a serial PC.
Then you generate the input for the linear response yambo_nl -u -V qp :

 nloptics                       # [R NL] Non-linear optics
 DIP_Threads=0                  # [OPENMP/X] Number of threads for dipoles
 NL_Threads=0                   # [OPENMP/NL] Number of threads for nl-optics
 % NLBands
   4 |  5 |                     # [NL] Bands
 %
 NLverbosity= "low"             # [NL] Verbosity level (low | high)
 NLstep=   0.0100       fs      # [NL] Real Time step length
 NLtime= 55.00000       fs      # [NL] Simulation Time
 NLintegrator= "CRANKNIC"         # [NL] Integrator ("EULEREXP/RK2/RK4/RK2EXP/HEUN/INVINT/CRANKNIC")
 NLCorrelation= "SEX"           # [NL] Correlation ("IPA/HARTREE/TDDFT/LRC/LRW/JGM/SEX")
 NLLrcAlpha= 0.000000           # [NL] Long Range Correction
 % NLEnRange
  0.200000 | 8.000000 | eV      # [NL] Energy range
 %
 NLEnSteps= 1                   # [NL] Energy steps
 NLDamping=  0.10000    eV      # [NL] Damping
 #UseDipoles                    # [NL] Use Covariant Dipoles (just for test purpose)
 #FrSndOrd                      # [NL] Force second order in Covariant Dipoles
 #EvalCurrent                   # [NL] Evaluate the current
 HARRLvcs= 1017         RL      # [HA] Hartree     RL components
 EXXRLvcs= 1074         mHa     # [XX] Exchange    RL components
 % ExtF_Dir
  0.000000 | 1.000000 | 0.000000 |        # [NL ExtF] Versor
 %
 ExtF_Int= 1000.        kWLm2   # [NL ExtF] Intensity
 ExtF_Width= 0.000000   fs      # [NL ExtF] Field Width
 ExtF_kind= "DELTA"             # [NL ExtF] Kind(SIN|SOFTSIN|RES|ANTIRES|GAUSS|DELTA|QSSIN)
 ExtF_Tstart=   0.0100  fs      # [NL ExtF] Initial Time
 % GfnQP_E
  3.000000 | 1.000000 | 1.000000 |        # [EXTQP G] E parameters  (c/v) eV|adim|adim
 %

Notice that we introduced a scissor operator (a rigid shift of the conduction bands) of 3.0 eV. In principle, it is possible to perform a G0W0 calculation with Yambo and use the Quasi-particle band structure instead of the rigid shift. Run this calculation and then analyze the result in the same way of linear response tutorial, you will get a nice exciton in hBN, as the one plotted below in the old tutorial. You can repeat the same kind of calculations for the non-linear response.
Notice that in the calculation we decreased the number of G-vectors in the Hartree term, '''NLGvecs''' to speed up the calculation, in case of BN this does not change the result because local field effects are very small in h-BN along the plane.
Now you can analyze the response with ypp as it was done the linear response tutorial and compare with the standard Bethe-Salpeter (input [[tutorials/lumen.in_bse|here]]): [[File:images/RT_BSE.png]] Input files for the linear response are available [[tutorials/lumen.in_bse|here]]. You can use the SEX approximation for the non-linear response too.