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https://github.com/pfloos/quack
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GW+C spectral function
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136
src/GW/GWC_spectral_function.f90
Normal file
136
src/GW/GWC_spectral_function.f90
Normal file
@ -0,0 +1,136 @@
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subroutine GWC_spectral_function(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
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! Plot the spectral function at the GW+C level
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implicit none
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include 'parameters.h'
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! Input variables
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integer,intent(in) :: nBas
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integer,intent(in) :: nC
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integer,intent(in) :: nO
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integer,intent(in) :: nV
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integer,intent(in) :: nR
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integer,intent(in) :: nS
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double precision,intent(in) :: eHF(nBas)
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double precision,intent(in) :: eGW(nBas)
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double precision,intent(in) :: Om(nS)
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double precision,intent(in) :: rho(nBas,nBas,nS)
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! Local variables
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double precision :: eta
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integer :: p,g
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integer :: nGrid
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double precision :: wmin,wmax,dw
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double precision,external :: GW_ReSigC,GW_ImSigC,GW_RedSigC,GW_ImdSigC
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double precision,allocatable :: w(:)
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double precision,allocatable :: ReSigC(:,:),ImSigC(:,:)
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double precision,allocatable :: RedSigC(:,:),ImdSigC(:,:)
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double precision,allocatable :: A(:,:)
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! Broadening parameter
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eta = 0.01d0
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! Construct grid
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nGrid = 5000
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allocate(w(nGrid),A(nBas,nGrid))
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! Minimum and maximum frequency values
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wmin = -5d0
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wmax = +5d0
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dw = (wmax - wmin)/dble(ngrid)
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do g=1,nGrid
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w(g) = wmin + dble(g)*dw
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end do
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! Compute QP part of the spectral function
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allocate(ReSigC(nBas,nGrid),ImSigC(nBas,nGrid))
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do g=1,nGrid
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do p=nC+1,nBas-nR
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ReSigC(p,g) = GW_ReSigC(p,eGW(p),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
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ImSigC(p,g) = GW_ImSigC(p,eGW(p),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
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end do
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end do
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do g=1,nGrid
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do p=nC+1,nBas-nR
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A(p,g) = abs(ImSigC(p,g))/((w(g) - eHF(p) - ReSigC(p,g))**2 + ImSigC(p,g)**2)
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end do
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end do
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A(:,:) = A(:,:)/pi
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deallocate(ReSigC,ImSigC)
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! Dump quantities in files as a function of w
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open(unit=11 ,file='GWC_AQP.dat')
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do g=1,nGrid
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write(11,*) w(g)*HaToeV,(A(p,g),p=nC+1,nBas-nR)
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end do
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! Closing files
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close(unit=11)
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! Compute cumulant part of the spectral function
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allocate(RedSigC(nBas,nGrid),ImdSigC(nBas,nGrid))
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do g=1,nGrid
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do p=nC+1,nBas-nR
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RedSigC(p,g) = GW_RedSigC(p,0d0,eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
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ImdSigC(p,g) = GW_ImdSigC(p,0d0,eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
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end do
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end do
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do g=1,nGrid
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do p=nC+1,nBas-nR
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A(p,g) = RedSigC(p,g) + (w(g) - eHF(p))*ImdSigC(p,g)
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end do
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end do
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do g=1,nGrid
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do p=nC+1,nBas-nR
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RedSigC(p,g) = GW_RedSigC(p,eHF(p)-w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
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end do
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end do
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do g=1,nGrid
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do p=nC+1,nBas-nR
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A(p,g) = (RedSigC(p,g) - A(p,g))/(w(g) - eHF(p))**2
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end do
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end do
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A(:,:) = A(:,:)/pi
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deallocate(RedSigC,ImdSigC)
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! Dump quantities in files as a function of w
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open(unit=12 ,file='GWC_AC.dat')
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do g=1,nGrid
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write(12,*) w(g)*HaToeV,(A(p,g),p=nC+1,nBas-nR)
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end do
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! Closing files
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close(unit=12)
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end subroutine
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@ -1,4 +1,4 @@
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double precision function GW_dSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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double precision function GW_ImdSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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! Compute the derivative of the correlation part of the self-energy
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@ -27,7 +27,7 @@ double precision function GW_dSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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! Initialize
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GW_dSigC = 0d0
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GW_ImdSigC = 0d0
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! Occupied part of the correlation self-energy
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@ -35,7 +35,7 @@ double precision function GW_dSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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do m=1,nS
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eps = w - e(i) + Om(m)
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num = 2d0*rho(p,i,m)**2
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GW_dSigC = GW_dSigC - num*(eps**2 - eta**2)/(eps**2 + eta**2)**2
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GW_ImdSigC = GW_ImdSigC - 2d0*num*eps*eta/(eps**2 + eta**2)**2
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end do
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end do
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@ -45,7 +45,7 @@ double precision function GW_dSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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do m=1,nS
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eps = w - e(a) - Om(m)
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num = 2d0*rho(p,a,m)**2
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GW_dSigC = GW_dSigC - num*(eps**2 - eta**2)/(eps**2 + eta**2)**2
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GW_ImdSigC = GW_ImdSigC + 2d0*num*eps*eta/(eps**2 + eta**2)**2
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end do
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end do
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@ -28,7 +28,7 @@ subroutine GW_QP_graph(eta,nBas,nC,nO,nV,nR,nS,eHF,Om,rho,eGWlin,eOld,eGW,Z)
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integer :: nIt
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integer,parameter :: maxIt = 64
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double precision,parameter :: thresh = 1d-6
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double precision,external :: GW_SigC,GW_dSigC
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double precision,external :: GW_ReSigC,GW_RedSigC
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double precision :: SigC,dSigC
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double precision :: f,df
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double precision :: w
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@ -54,8 +54,8 @@ subroutine GW_QP_graph(eta,nBas,nC,nO,nV,nR,nS,eHF,Om,rho,eGWlin,eOld,eGW,Z)
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nIt = nIt + 1
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SigC = GW_SigC(p,w,eta,nBas,nC,nO,nV,nR,nS,eOld,Om,rho)
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dSigC = GW_dSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,eOld,Om,rho)
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SigC = GW_ReSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,eOld,Om,rho)
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dSigC = GW_RedSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,eOld,Om,rho)
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f = w - eHF(p) - SigC
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df = 1d0/(1d0 - dSigC)
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w = w - df*f
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@ -1,4 +1,4 @@
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double precision function GW_SigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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double precision function GW_ReSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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! Compute diagonal of the correlation part of the self-energy
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@ -27,7 +27,7 @@ double precision function GW_SigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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! Initialize
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GW_SigC = 0d0
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GW_ReSigC = 0d0
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! Occupied part of the correlation self-energy
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@ -35,7 +35,7 @@ double precision function GW_SigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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do m=1,nS
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eps = w - e(i) + Om(m)
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num = 2d0*rho(p,i,m)**2
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GW_SigC = GW_SigC + num*eps/(eps**2 + eta**2)
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GW_ReSigC = GW_ReSigC + num*eps/(eps**2 + eta**2)
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end do
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end do
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@ -45,7 +45,7 @@ double precision function GW_SigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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do m=1,nS
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eps = w - e(a) - Om(m)
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num = 2d0*rho(p,a,m)**2
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GW_SigC = GW_SigC + num*eps/(eps**2 + eta**2)
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GW_ReSigC = GW_ReSigC + num*eps/(eps**2 + eta**2)
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end do
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end do
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52
src/GW/GW_RedSigC.f90
Normal file
52
src/GW/GW_RedSigC.f90
Normal file
@ -0,0 +1,52 @@
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double precision function GW_RedSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
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! Compute the derivative of the correlation part of the self-energy
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implicit none
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include 'parameters.h'
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! Input variables
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integer,intent(in) :: p
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double precision,intent(in) :: w
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double precision,intent(in) :: eta
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integer,intent(in) :: nBas
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integer,intent(in) :: nC
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integer,intent(in) :: nO
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integer,intent(in) :: nV
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integer,intent(in) :: nR
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integer,intent(in) :: nS
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double precision,intent(in) :: e(nBas)
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double precision,intent(in) :: Om(nS)
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double precision,intent(in) :: rho(nBas,nBas,nS)
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! Local variables
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integer :: i,a,m
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double precision :: num,eps
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! Initialize
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GW_RedSigC = 0d0
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! Occupied part of the correlation self-energy
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do i=nC+1,nO
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do m=1,nS
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eps = w - e(i) + Om(m)
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num = 2d0*rho(p,i,m)**2
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GW_RedSigC = GW_RedSigC - num*(eps**2 - eta**2)/(eps**2 + eta**2)**2
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end do
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end do
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! Virtual part of the correlation self-energy
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do a=nO+1,nBas-nR
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do m=1,nS
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eps = w - e(a) - Om(m)
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num = 2d0*rho(p,a,m)**2
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GW_RedSigC = GW_RedSigC - num*(eps**2 - eta**2)/(eps**2 + eta**2)**2
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end do
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end do
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end function
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@ -24,11 +24,11 @@ subroutine GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
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integer :: p,g
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integer :: nGrid
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double precision :: wmin,wmax,dw
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double precision,external :: GW_SigC,GW_ImSigC,GW_dSigC
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double precision,external :: GW_ReSigC,GW_ImSigC,GW_RedSigC
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double precision,allocatable :: w(:)
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double precision,allocatable :: ReSigC(:,:),ImSigC(:,:)
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double precision,allocatable :: Z(:,:)
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double precision,allocatable :: S(:,:)
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double precision,allocatable :: A(:,:)
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! Broadening parameter
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@ -37,7 +37,7 @@ subroutine GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
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! Construct grid
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nGrid = 5000
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allocate(w(nGrid),ReSigC(nBas,nGrid),ImSigC(nBas,nGrid),Z(nBas,nGrid),S(nBas,nGrid))
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allocate(w(nGrid),ReSigC(nBas,nGrid),ImSigC(nBas,nGrid),Z(nBas,nGrid),A(nBas,nGrid))
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! Initialize
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@ -60,9 +60,9 @@ subroutine GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
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do g=1,nGrid
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do p=nC+1,nBas-nR
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ReSigC(p,g) = GW_SigC(p,w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
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ReSigC(p,g) = GW_ReSigC(p,w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
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ImSigC(p,g) = GW_ImSigC(p,w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
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Z(p,g) = GW_dSigC(p,w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
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Z(p,g) = GW_RedSigC(p,w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
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end do
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end do
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@ -73,11 +73,11 @@ subroutine GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
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do g=1,nGrid
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do p=nC+1,nBas-nR
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S(p,g) = abs(ImSigC(p,g))/((w(g) - eHF(p) - ReSigC(p,g))**2 + ImSigC(p,g)**2)
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A(p,g) = abs(ImSigC(p,g))/((w(g) - eHF(p) - ReSigC(p,g))**2 + ImSigC(p,g)**2)
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end do
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end do
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S(:,:) = S(:,:)/pi
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A(:,:) = A(:,:)/pi
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! Dump quantities in files as a function of w
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@ -90,7 +90,7 @@ subroutine GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
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write(8 ,*) w(g)*HaToeV,(ReSigC(p,g)*HaToeV,p=nC+1,nBas-nR)
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write(9 ,*) w(g)*HaToeV,((w(g)-eHF(p))*HaToeV,p=nC+1,nBas-nR)
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write(10,*) w(g)*HaToeV,(Z(p,g),p=nC+1,nBas-nR)
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write(11,*) w(g)*HaToeV,(S(p,g),p=nC+1,nBas-nR)
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write(11,*) w(g)*HaToeV,(A(p,g),p=nC+1,nBas-nR)
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end do
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! Closing files
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@ -146,13 +146,16 @@ subroutine RG0W0(dotest,doACFDT,exchange_kernel,doXBS,dophBSE,dophBSE2,TDA_W,TDA
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end if
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! Plot self-energy, renormalization factor, and spectral function
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call GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eHF,Om,rho)
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!--------------------!
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! Cumulant expansion !
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!--------------------!
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call RGWC(dotest,nBas,nC,nO,nR,nS,Om,rho,eGW,Z)
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! call GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eHF,Om,rho)
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call GWC_spectral_function(nBas,nC,nO,nV,nR,nS,eHF,eHF,Om,rho)
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! Compute the RPA correlation energy
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