CalculateSelfEnergy

ResponseFunction.CalculateSelfEnergy($G_0$,$G$) calculates \begin{equation} \Sigma = G_0^{-1} - G^{-1} \end{equation}

• $G_0$ : ResponseFunction object
• $G$ : ResponseFunction object
• Possible options are:

  • “epsilon” : minimal distance between two poles to be considered different in energy (default value 2.3E-13)

• $\Sigma$ : ResponseFunction object

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CalculateSelfEnergy.Quanty

-- H0, H1, Npsi, TPes, TIPes are defined beforehand
psiList = Eigensystem(H0,StartRestrictions, Npsi)
 
G0PESIPES_Spectra, G0PESIPES_ResponseFunction = CreateSpectra(H0, {TPes, TIPes}, psiList[1], {{"Emin",-1}, {"Emax",9}, {"NE",1000}, {"Gamma",0.25}})
G0 = G0PESIPES_ResponseFunction[2]  + ResponseFunction.InvertEnergy(G0PESIPES_ResponseFunction[1])
 
Eigensystem(H0+H1, psiList[1]) -- Use H0 groundstate as Ansatz for Full Hamiltonian groundstate calculation
--For memory efficiency, this way of calling Eigensystem overwrites Ansatz wavefunction with a new one.  
 
GPESIPES_Spectra, GPESIPES_ResponseFunction = CreateSpectra(H0+H1, {TPes, TIPes}, psiList[1], {{"Emin",-1}, {"Emax",9}, {"NE",1000}, {"Gamma",0.25}})
G = GPESIPES_ResponseFunction[2]  + ResponseFunction.InvertEnergy(GPESIPES_ResponseFunction[1])
 
Sigma = ResponseFunction.CalculateSelfEnergy(G0,G)
 
print(ResponseFunction.ToTable(Sigma))

{ { 0.5 , 6.9374060711003e-16 , 3.0413812651491 } , 
  { 0.085601012694643 , 0.16439898730536 } ,
  name = Self energy ,
  mu = 0 ,
  type = ListOfPoles }