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GW+C spectral function

This commit is contained in:
Pierre-Francois Loos 2024-01-29 17:20:57 +01:00
parent c2fc694fdb
commit 6680cc84dd
7 changed files with 212 additions and 21 deletions
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136
src/GW/GWC_spectral_function.f90 Normal file
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@ -0,0 +1,136 @@
subroutine GWC_spectral_function(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
! Plot the spectral function at the GW+C level
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: nBas
integer,intent(in) :: nC
integer,intent(in) :: nO
integer,intent(in) :: nV
integer,intent(in) :: nR
integer,intent(in) :: nS
double precision,intent(in) :: eHF(nBas)
double precision,intent(in) :: eGW(nBas)
double precision,intent(in) :: Om(nS)
double precision,intent(in) :: rho(nBas,nBas,nS)
! Local variables
double precision :: eta
integer :: p,g
integer :: nGrid
double precision :: wmin,wmax,dw
double precision,external :: GW_ReSigC,GW_ImSigC,GW_RedSigC,GW_ImdSigC
double precision,allocatable :: w(:)
double precision,allocatable :: ReSigC(:,:),ImSigC(:,:)
double precision,allocatable :: RedSigC(:,:),ImdSigC(:,:)
double precision,allocatable :: A(:,:)
! Broadening parameter
eta = 0.01d0
! Construct grid
nGrid = 5000
allocate(w(nGrid),A(nBas,nGrid))
! Minimum and maximum frequency values
wmin = -5d0
wmax = +5d0
dw = (wmax - wmin)/dble(ngrid)
do g=1,nGrid
w(g) = wmin + dble(g)*dw
end do
! Compute QP part of the spectral function
allocate(ReSigC(nBas,nGrid),ImSigC(nBas,nGrid))
do g=1,nGrid
do p=nC+1,nBas-nR
ReSigC(p,g) = GW_ReSigC(p,eGW(p),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
ImSigC(p,g) = GW_ImSigC(p,eGW(p),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
end do
end do
do g=1,nGrid
do p=nC+1,nBas-nR
A(p,g) = abs(ImSigC(p,g))/((w(g) - eHF(p) - ReSigC(p,g))**2 + ImSigC(p,g)**2)
end do
end do
A(:,:) = A(:,:)/pi
deallocate(ReSigC,ImSigC)
! Dump quantities in files as a function of w
open(unit=11 ,file='GWC_AQP.dat')
do g=1,nGrid
write(11,*) w(g)*HaToeV,(A(p,g),p=nC+1,nBas-nR)
end do
! Closing files
close(unit=11)
! Compute cumulant part of the spectral function
allocate(RedSigC(nBas,nGrid),ImdSigC(nBas,nGrid))
do g=1,nGrid
do p=nC+1,nBas-nR
RedSigC(p,g) = GW_RedSigC(p,0d0,eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
ImdSigC(p,g) = GW_ImdSigC(p,0d0,eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
end do
end do
do g=1,nGrid
do p=nC+1,nBas-nR
A(p,g) = RedSigC(p,g) + (w(g) - eHF(p))*ImdSigC(p,g)
end do
end do
do g=1,nGrid
do p=nC+1,nBas-nR
RedSigC(p,g) = GW_RedSigC(p,eHF(p)-w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
end do
end do
do g=1,nGrid
do p=nC+1,nBas-nR
A(p,g) = (RedSigC(p,g) - A(p,g))/(w(g) - eHF(p))**2
end do
end do
A(:,:) = A(:,:)/pi
deallocate(RedSigC,ImdSigC)
! Dump quantities in files as a function of w
open(unit=12 ,file='GWC_AC.dat')
do g=1,nGrid
write(12,*) w(g)*HaToeV,(A(p,g),p=nC+1,nBas-nR)
end do
! Closing files
close(unit=12)
end subroutine

8
src/GW/GW_dSigC.f90 → src/GW/GW_ImdSigC.f90
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@ -1,4 +1,4 @@
double precision function GW_dSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
double precision function GW_ImdSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
! Compute the derivative of the correlation part of the self-energy
@ -27,7 +27,7 @@ double precision function GW_dSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
! Initialize
GW_dSigC = 0d0
GW_ImdSigC = 0d0
! Occupied part of the correlation self-energy
@ -35,7 +35,7 @@ double precision function GW_dSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
do m=1,nS
eps = w - e(i) + Om(m)
num = 2d0*rho(p,i,m)**2
GW_dSigC = GW_dSigC - num*(eps**2 - eta**2)/(eps**2 + eta**2)**2
GW_ImdSigC = GW_ImdSigC - 2d0*num*eps*eta/(eps**2 + eta**2)**2
end do
end do
@ -45,7 +45,7 @@ double precision function GW_dSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
do m=1,nS
eps = w - e(a) - Om(m)
num = 2d0*rho(p,a,m)**2
GW_dSigC = GW_dSigC - num*(eps**2 - eta**2)/(eps**2 + eta**2)**2
GW_ImdSigC = GW_ImdSigC + 2d0*num*eps*eta/(eps**2 + eta**2)**2
end do
end do

6
src/GW/GW_QP_graph.f90
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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)
integer :: nIt
integer,parameter :: maxIt = 64
double precision,parameter :: thresh = 1d-6
double precision,external :: GW_SigC,GW_dSigC
double precision,external :: GW_ReSigC,GW_RedSigC
double precision :: SigC,dSigC
double precision :: f,df
double precision :: w
@ -54,8 +54,8 @@ subroutine GW_QP_graph(eta,nBas,nC,nO,nV,nR,nS,eHF,Om,rho,eGWlin,eOld,eGW,Z)
nIt = nIt + 1
SigC = GW_SigC(p,w,eta,nBas,nC,nO,nV,nR,nS,eOld,Om,rho)
dSigC = GW_dSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,eOld,Om,rho)
SigC = GW_ReSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,eOld,Om,rho)
dSigC = GW_RedSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,eOld,Om,rho)
f = w - eHF(p) - SigC
df = 1d0/(1d0 - dSigC)
w = w - df*f

8
src/GW/GW_SigC.f90 → src/GW/GW_ReSigC.f90
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@ -1,4 +1,4 @@
double precision function GW_SigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
double precision function GW_ReSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
! Compute diagonal of the correlation part of the self-energy
@ -27,7 +27,7 @@ double precision function GW_SigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
! Initialize
GW_SigC = 0d0
GW_ReSigC = 0d0
! Occupied part of the correlation self-energy
@ -35,7 +35,7 @@ double precision function GW_SigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
do m=1,nS
eps = w - e(i) + Om(m)
num = 2d0*rho(p,i,m)**2
GW_SigC = GW_SigC + num*eps/(eps**2 + eta**2)
GW_ReSigC = GW_ReSigC + num*eps/(eps**2 + eta**2)
end do
end do
@ -45,7 +45,7 @@ double precision function GW_SigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
do m=1,nS
eps = w - e(a) - Om(m)
num = 2d0*rho(p,a,m)**2
GW_SigC = GW_SigC + num*eps/(eps**2 + eta**2)
GW_ReSigC = GW_ReSigC + num*eps/(eps**2 + eta**2)
end do
end do

52
src/GW/GW_RedSigC.f90 Normal file
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@ -0,0 +1,52 @@
double precision function GW_RedSigC(p,w,eta,nBas,nC,nO,nV,nR,nS,e,Om,rho)
! Compute the derivative of the correlation part of the self-energy
implicit none
include 'parameters.h'
! Input variables
integer,intent(in) :: p
double precision,intent(in) :: w
double precision,intent(in) :: eta
integer,intent(in) :: nBas
integer,intent(in) :: nC
integer,intent(in) :: nO
integer,intent(in) :: nV
integer,intent(in) :: nR
integer,intent(in) :: nS
double precision,intent(in) :: e(nBas)
double precision,intent(in) :: Om(nS)
double precision,intent(in) :: rho(nBas,nBas,nS)
! Local variables
integer :: i,a,m
double precision :: num,eps
! Initialize
GW_RedSigC = 0d0
! Occupied part of the correlation self-energy
do i=nC+1,nO
do m=1,nS
eps = w - e(i) + Om(m)
num = 2d0*rho(p,i,m)**2
GW_RedSigC = GW_RedSigC - num*(eps**2 - eta**2)/(eps**2 + eta**2)**2
end do
end do
! Virtual part of the correlation self-energy
do a=nO+1,nBas-nR
do m=1,nS
eps = w - e(a) - Om(m)
num = 2d0*rho(p,a,m)**2
GW_RedSigC = GW_RedSigC - num*(eps**2 - eta**2)/(eps**2 + eta**2)**2
end do
end do
end function

16
src/GW/GW_plot_self_energy.f90
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@ -24,11 +24,11 @@ subroutine GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
integer :: p,g
integer :: nGrid
double precision :: wmin,wmax,dw
double precision,external :: GW_SigC,GW_ImSigC,GW_dSigC
double precision,external :: GW_ReSigC,GW_ImSigC,GW_RedSigC
double precision,allocatable :: w(:)
double precision,allocatable :: ReSigC(:,:),ImSigC(:,:)
double precision,allocatable :: Z(:,:)
double precision,allocatable :: S(:,:)
double precision,allocatable :: A(:,:)
! Broadening parameter
@ -37,7 +37,7 @@ subroutine GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
! Construct grid
nGrid = 5000
allocate(w(nGrid),ReSigC(nBas,nGrid),ImSigC(nBas,nGrid),Z(nBas,nGrid),S(nBas,nGrid))
allocate(w(nGrid),ReSigC(nBas,nGrid),ImSigC(nBas,nGrid),Z(nBas,nGrid),A(nBas,nGrid))
! Initialize
@ -60,9 +60,9 @@ subroutine GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
do g=1,nGrid
do p=nC+1,nBas-nR
ReSigC(p,g) = GW_SigC(p,w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
ReSigC(p,g) = GW_ReSigC(p,w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
ImSigC(p,g) = GW_ImSigC(p,w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
Z(p,g) = GW_dSigC(p,w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
Z(p,g) = GW_RedSigC(p,w(g),eta,nBas,nC,nO,nV,nR,nS,eGW,Om,rho)
end do
end do
@ -73,11 +73,11 @@ subroutine GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
do g=1,nGrid
do p=nC+1,nBas-nR
S(p,g) = abs(ImSigC(p,g))/((w(g) - eHF(p) - ReSigC(p,g))**2 + ImSigC(p,g)**2)
A(p,g) = abs(ImSigC(p,g))/((w(g) - eHF(p) - ReSigC(p,g))**2 + ImSigC(p,g)**2)
end do
end do
S(:,:) = S(:,:)/pi
A(:,:) = A(:,:)/pi
! Dump quantities in files as a function of w
@ -90,7 +90,7 @@ subroutine GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eGW,Om,rho)
write(8 ,*) w(g)*HaToeV,(ReSigC(p,g)*HaToeV,p=nC+1,nBas-nR)
write(9 ,*) w(g)*HaToeV,((w(g)-eHF(p))*HaToeV,p=nC+1,nBas-nR)
write(10,*) w(g)*HaToeV,(Z(p,g),p=nC+1,nBas-nR)
write(11,*) w(g)*HaToeV,(S(p,g),p=nC+1,nBas-nR)
write(11,*) w(g)*HaToeV,(A(p,g),p=nC+1,nBas-nR)
end do
! Closing files

7
src/GW/RG0W0.f90
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@ -146,13 +146,16 @@ subroutine RG0W0(dotest,doACFDT,exchange_kernel,doXBS,dophBSE,dophBSE2,TDA_W,TDA
end if
! Plot self-energy, renormalization factor, and spectral function
call GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eHF,Om,rho)
!--------------------!
! Cumulant expansion !
!--------------------!
call RGWC(dotest,nBas,nC,nO,nR,nS,Om,rho,eGW,Z)
! call GW_plot_self_energy(nBas,nC,nO,nV,nR,nS,eHF,eHF,Om,rho)
call GWC_spectral_function(nBas,nC,nO,nV,nR,nS,eHF,eHF,Om,rho)
! Compute the RPA correlation energy