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ED_OBSERVABLES.f90
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MODULE ED_OBSERVABLES
USE SF_CONSTANTS, only:zero,pi,xi
USE SF_IOTOOLS, only:free_unit,reg,txtfy
USE SF_ARRAYS, only: arange
USE SF_INTEGRATE, only: quad
USE SF_LINALG
USE ED_INPUT_VARS
USE ED_VARS_GLOBAL
USE ED_EIGENSPACE
USE ED_SETUP
USE ED_HAMILTONIAN
USE ED_BATH
USE ED_AUX_FUNX
USE ED_IO
USE ED_BATH_FUNCTIONS
implicit none
private
!
interface add_custom_observable
module procedure :: add_custom_observable_local
module procedure :: add_custom_observable_kdep
end interface add_custom_observable
public :: observables_impurity
public :: local_energy_impurity
public :: init_custom_observables
public :: add_custom_observable
public :: get_custom_observables
public :: clear_custom_observables
logical,save :: iolegend=.true.
real(8),dimension(:,:),allocatable :: dens,dens_up,dens_dw
real(8),dimension(:,:),allocatable :: docc
real(8),dimension(:,:),allocatable :: magz
real(8),dimension(:,:,:,:),allocatable :: sz2,n2
real(8),dimension(:,:,:),allocatable :: zimp,simp
real(8),dimension(:),allocatable :: s2tot
real(8) :: Egs
real(8) :: Ei
real(8) :: integrationR
complex(8),allocatable,dimension(:,:,:) :: sij
complex(8),allocatable,dimension(:,:,:) :: Hk
!
integer :: iorb,jorb,iorb1,jorb1
integer :: ispin,jspin
integer :: ilat,jlat
integer :: ibath
integer :: r,m,k,k1,k2
integer :: iup,idw
integer :: jup,jdw
integer :: mup,mdw
real(8) :: sgn,sgn1,sgn2,sg1,sg2
real(8) :: gs_weight
!
real(8) :: peso
real(8) :: norm
!
integer :: i,j,ii
integer :: isector,jsector
integer :: idim,idimUP,idimDW
!
complex(8),dimension(:),pointer :: state_cvec
logical :: Jcondition
!
contains
!+-------------------------------------------------------------------+
!PURPOSE : Evaluate and print out many interesting physical qties
!+-------------------------------------------------------------------+
subroutine observables_impurity()
call lanc_observables()
end subroutine observables_impurity
subroutine local_energy_impurity()
call lanc_local_energy()
end subroutine local_energy_impurity
subroutine init_custom_observables(N,Hk)
integer :: N
complex(8),dimension(:,:,:) :: Hk
!
if(MpiMaster)then
custom_o%N_filled=0
custom_o%N_asked=N
allocate(custom_o%Hk(size(Hk,1),size(Hk,2),size(Hk,3)))
custom_o%Hk=Hk
allocate(custom_o%item(N))
custom_o%init=.true.
endif
!
end subroutine init_custom_observables
subroutine add_custom_observable_local(o_name,sij)
integer :: i
complex(8),dimension(:,:) :: sij
character(len=*) :: o_name
!
if(MpiMaster .and. custom_o%init)then
if(custom_o%N_filled .gt. custom_o%N_asked)then
STOP "add_custom_observable: too many observables given"
call clear_custom_observables
endif
!
custom_o%N_filled=custom_o%N_filled+1
custom_o%item(custom_o%N_filled)%o_name=o_name
custom_o%item(custom_o%N_filled)%o_value=0.d0
!
allocate(custom_o%item(custom_o%N_filled)%sij(size(custom_o%Hk,1),size(custom_o%Hk,2),size(custom_o%Hk,3)))
do i=1,size(custom_o%item(custom_o%N_filled)%sij,3)
custom_o%item(custom_o%N_filled)%sij(:,:,i)=sij
enddo
else
STOP "add_custom_observable: custom observables not initialized"
endif
end subroutine add_custom_observable_local
subroutine add_custom_observable_kdep(o_name,sijk)
integer :: i
complex(8),dimension(:,:,:) :: sijk
character(len=*) :: o_name
!
if(MpiMaster .and. custom_o%init)then
if(custom_o%N_filled .gt. custom_o%N_asked)then
STOP "add_custom_observable: too many observables given"
call clear_custom_observables
endif
!
custom_o%N_filled=custom_o%N_filled+1
custom_o%item(custom_o%N_filled)%o_name=o_name
custom_o%item(custom_o%N_filled)%o_value=0.d0
!
allocate(custom_o%item(custom_o%N_filled)%sij(size(custom_o%Hk,1),size(custom_o%Hk,2),size(custom_o%Hk,3)))
custom_o%item(custom_o%N_filled)%sij=sijk
else
STOP "add_custom_observable: custom observables not initialized"
endif
end subroutine add_custom_observable_kdep
subroutine get_custom_observables()
integer :: i
!
if(MpiMaster .and. custom_o%init)then
if(custom_o%N_filled .eq. 0)then
write(Logfile,*)"WARNING! Custom observables initialized but none given."
RETURN
endif
!
write(LOGfile,*)"Calculating custom observables"
!
allocate(sij(size(custom_o%Hk,1),size(custom_o%Hk,2),size(custom_o%Hk,3)))
allocate(Hk(size(custom_o%Hk,1),size(custom_o%Hk,2),size(custom_o%Hk,3)))
sij=zero
Hk=zero
!
Hk=custom_o%Hk
do i=1,custom_o%N_filled
sij=custom_o%item(i)%sij
if(finiteT) then
custom_o%item(i)%o_value=calculate_observable_integral_finite_t()
else
custom_o%item(i)%o_value=calculate_observable_integral_zero_t()
endif
write(LOGfile,"(A,10f18.12,A)")reg(custom_o%item(i)%o_name)//" = ",custom_o%item(i)%o_value
enddo
call write_custom_legend()
call write_custom_observables()
deallocate(sij,Hk)
endif
!
end subroutine get_custom_observables
subroutine clear_custom_observables()
integer :: i
if(MpiMaster .and. custom_o%init)then
do i=1,custom_o%N_filled
deallocate(custom_o%item(i)%sij)
custom_o%item(i)%o_name=""
custom_o%item(i)%o_value=0.d0
enddo
deallocate(custom_o%Hk)
custom_o%N_asked=0
custom_o%N_filled=0
custom_o%init=.false.
endif
end subroutine clear_custom_observables
!+-------------------------------------------------------------------+
!PURPOSE : Lanc method
!+-------------------------------------------------------------------+
subroutine lanc_observables()
integer :: istate,Nud(2,Ns),iud(2),jud(2),is,js
integer,dimension(2*Ns_Ud) :: Indices,Jndices
integer,dimension(Ns_Ud) :: iDimUps,iDimDws
integer,dimension(Ns) :: IbUp,IbDw ![Ns]
real(8),dimension(Nlat,Norb) :: nup,ndw,Sz,nt
type(sector_map),dimension(2*Ns_Ud) :: HI
!
!LOCAL OBSERVABLES:
allocate(dens(Nlat,Norb),dens_up(Nlat,Norb),dens_dw(Nlat,Norb))
allocate(docc(Nlat,Norb),s2tot(Nlat))
allocate(magz(Nlat,Norb),sz2(Nlat,Nlat,Norb,Norb),n2(Nlat,Nlat,Norb,Norb))
allocate(simp(Nlat,Norb,Nspin),zimp(Nlat,Norb,Nspin))
!
Egs = state_list%emin
dens = 0.d0
dens_up = 0.d0
dens_dw = 0.d0
docc = 0.d0
magz = 0.d0
sz2 = 0.d0
n2 = 0.d0
s2tot = 0.d0
!
do istate=1,state_list%size
isector = es_return_sector(state_list,istate)
Ei = es_return_energy(state_list,istate)
!
#ifdef _MPI
if(MpiStatus)then
state_cvec => es_return_cvector(MpiComm,state_list,istate)
else
state_cvec => es_return_cvector(state_list,istate)
endif
#else
state_cvec => es_return_cvector(state_list,istate)
#endif
!
!
peso = 1.d0 ; if(finiteT)peso=exp(-beta*(Ei-Egs))
peso = peso/zeta_function
!
iDim = getdim(isector)
call get_DimUp(isector,iDimUps)
call get_DimDw(isector,iDimDws)
iDimUp = product(iDimUps)
iDimDw = product(iDimDws)
!
if(MpiMaster)then
call build_sector(isector,HI)
do i = 1,iDim
call state2indices(i,[iDimUps,iDimDws],Indices)
do ii=1,Ns_Ud
mup = HI(ii)%map(Indices(ii))
mdw = HI(ii+Ns_Ud)%map(Indices(ii+Ns_ud))
IbUp = Bdecomp(mup,Ns_Orb) ![Norb,1+Nbath]
IbDw = Bdecomp(mdw,Ns_Orb)
enddo
!
gs_weight=peso*abs(state_cvec(i))**2
!
!Get operators:
do ilat=1,Nlat
do iorb=1,Norb
nup(ilat,iorb)= ibup(imp_state_index(ilat,iorb))
ndw(ilat,iorb)= ibdw(imp_state_index(ilat,iorb))
sz(ilat,iorb) = (nup(ilat,iorb) - ndw(ilat,iorb))/2d0
nt(ilat,iorb) = nup(ilat,iorb) + ndw(ilat,iorb)
enddo
enddo
!
!Evaluate averages of observables:
!>TODO:
!add non-local averges like spin-spin, density-density etc...
!<TODO
do ilat=1,Nlat
do iorb=1,Norb
dens(ilat,iorb) = dens(ilat,iorb) + nt(ilat,iorb)*gs_weight
dens_up(ilat,iorb) = dens_up(ilat,iorb) + nup(ilat,iorb)*gs_weight
dens_dw(ilat,iorb) = dens_dw(ilat,iorb) + ndw(ilat,iorb)*gs_weight
docc(ilat,iorb) = docc(ilat,iorb) + nup(ilat,iorb)*ndw(ilat,iorb)*gs_weight
magz(ilat,iorb) = magz(ilat,iorb) + (nup(ilat,iorb)-ndw(ilat,iorb))*gs_weight
enddo
s2tot(ilat) = s2tot(ilat) + (sum(sz(ilat,:)))**2*gs_weight
enddo
do ilat=1,Nlat
do iorb=1,Norb
sz2(ilat,ilat,iorb,iorb) = sz2(ilat,ilat,iorb,iorb) + (sz(ilat,iorb)*sz(ilat,iorb))*gs_weight
n2(ilat,ilat,iorb,iorb) = n2(ilat,ilat,iorb,iorb) + (nt(ilat,iorb)*nt(ilat,iorb))*gs_weight
do jlat=1,Nlat
do jorb=iorb+1,Norb
sz2(ilat,jlat,iorb,jorb) = sz2(ilat,jlat,iorb,jorb) + (sz(ilat,iorb)*sz(jlat,jorb))*gs_weight
sz2(ilat,jlat,jorb,iorb) = sz2(ilat,jlat,jorb,iorb) + (sz(ilat,jorb)*sz(jlat,iorb))*gs_weight
n2(ilat,jlat,iorb,jorb) = n2(ilat,jlat,iorb,jorb) + (nt(ilat,iorb)*nt(jlat,jorb))*gs_weight
n2(ilat,jlat,jorb,iorb) = n2(ilat,jlat,jorb,iorb) + (nt(jlat,jorb)*nt(ilat,iorb))*gs_weight
enddo
enddo
enddo
enddo
enddo
call delete_sector(isector,HI)
endif
!
#ifdef _MPI
if(MpiStatus)then
if(associated(state_cvec))deallocate(state_cvec)
else
if(associated(state_cvec))nullify(state_cvec)
endif
#else
if(associated(state_cvec))nullify(state_cvec)
#endif
!
enddo
!
!
!
if(MPIMASTER)then
call get_szr
if(iolegend)call write_legend
call write_observables()
!
do ilat=1,Nlat
write(LOGfile,"(A,10f18.12,f18.12,A)")"dens site "//str(ilat)//" "//reg(ed_file_suffix)//"=",(dens(ilat,iorb),iorb=1,Norb),sum(dens(ilat,:))
enddo
write(LOGfile,"(A,10f18.12,f18.12,A)")"dens avg "//reg(ed_file_suffix)//" =",(sum(dens(:,iorb))/Nlat,iorb=1,Norb),sum(dens)/Nlat
!
write(LOGfile,"(A,10f18.12,A)")"docc "//reg(ed_file_suffix)//" =",(sum(docc(:,iorb))/Nlat,iorb=1,Norb)
if(Nspin==2)write(LOGfile,"(A,10f18.12,A)") "mag "//reg(ed_file_suffix)//"=",(sum(magz(:,iorb))/Nlat,iorb=1,Norb)
!
ed_dens_up=dens_up
ed_dens_dw=dens_dw
ed_dens =dens
ed_docc =docc
endif
#ifdef _MPI
if(MpiStatus)then
call Bcast_MPI(MpiComm,ed_dens_up)
call Bcast_MPI(MpiComm,ed_dens_dw)
call Bcast_MPI(MpiComm,ed_dens)
call Bcast_MPI(MpiComm,ed_docc)
endif
#endif
!
deallocate(dens,docc,dens_up,dens_dw,magz,sz2,n2,s2tot)
deallocate(simp,zimp)
end subroutine lanc_observables
!+---------------------------------------------------------------------------------+
!PURPOSE : Evaluate and print out custom observable
!+---------------------------------------------------------------------------------+
!T=0
function calculate_observable_integral_zero_t() result(out_2)
integer :: inf
real(8) :: out_2,spin_multiplicity
!
out_2=0.d0
spin_multiplicity=3.d0-Nspin
!
call quad(sum_observable_kmesh,a=0.0d0,inf=1,verbose=(ED_VERBOSE>=3),result=out_2,strict=.false.)
!
out_2=spin_multiplicity*out_2/pi
return
end function calculate_observable_integral_zero_t
!T finite
function calculate_observable_integral_finite_t() result(out_2)
integer :: inf,Nmax,ii
real(8) :: out_2,spin_multiplicity,omegamax,integralpart
!
!1) Find the real omegamax
nmax=int(2*(abs(max_exc)+2.d0*hwband)*beta/pi)
if (mod(nmax,2)==0)then
nmax=nmax/2
else
nmax=(nmax+1)/2
endif
integrationR=2*(nmax+1)*pi/beta
!2) Evaluate discrete sum
!
out_2=0.d0
do ii=0,Nmax
out_2=out_2+dreal(sum_observable_kmesh_complex(xi*(2*ii+1)*pi/beta))
enddo
!
out_2=2.d0*(1/beta)*out_2
!
!3) Evaluate integral part
integralpart=0.d0
call quad(integral_contour,a=-pi,b=pi,verbose=(ED_VERBOSE>=3),key=6,result=integralpart,strict=.false.)
!
!4) Sum all
out_2=out_2+integralpart
!5) Spin trick
spin_multiplicity=3.d0-Nspin
out_2=spin_multiplicity*out_2
return
end function calculate_observable_integral_finite_t
function integral_contour(zeta) result(f)
real(8) :: zeta,f
complex(8) :: w,fermi
!
w=integrationR*exp(xi*zeta)
if(dreal((w-XMU)*beta)>= 100)then
fermi=0.d0
else
fermi=(1/(exp(beta*(w-XMU))+1))
endif
!
f=dreal((1.d0/pi)*w*fermi*sum_observable_kmesh_complex(w))
end function integral_contour
!+-------------------------------------------------------------------+
!PURPOSE : sum on k-vectors
!+-------------------------------------------------------------------+
function sum_observable_kmesh(omega) result(out_1)
integer :: ii,jj,kk
real(8) :: omega
real(8) :: out_1
complex(8),dimension(Nlat,Nlat,Nspin,Nspin,Norb,Norb) :: g,invg0
complex(8),dimension(Nlat*Nspin*Norb,Nlat*Nspin*Norb) :: invg_lso,invg0_lso,sigma,Gk_lso
!
out_1=0.d0
!
g=zero
invg0=zero
invg_lso=zero
invg0_lso=zero
Gk_lso=zero
Sigma=zero
!
!Obtain Sigma(iw)
call ed_gf_cluster(dcmplx(0.d0,omega),g)
invg_lso=nnn2lso_reshape(g,Nlat,Nspin,Norb)
call inv(invg_lso)
invg0=invg0_bath(dcmplx(0.d0,omega))
invg0_lso=nnn2lso_reshape(invg0,Nlat,Nspin,Norb)
Sigma=invg0_lso-invg_lso
!
!Do the k-sum
do ii=1,size(Hk,3)
Gk_lso=(dcmplx(0d0,omega)+xmu)*eye(Nlat*Nspin*Norb) - Hk(:,:,ii) - Sigma
call inv(Gk_lso)
out_1=out_1+DREAL(trace(matmul(sij(:,:,ii),Gk_lso)) - trace(sij(:,:,ii))/(dcmplx(-1.1d0,omega)))
enddo
!
out_1=out_1/(size(Hk,3))
!
return
!
end function sum_observable_kmesh
function sum_observable_kmesh_complex(omega) result(out_1)
integer :: ii,jj,kk
complex(8) :: omega
complex(8) :: out_1
complex(8),dimension(Nlat,Nlat,Nspin,Nspin,Norb,Norb) :: g,invg0
complex(8),dimension(Nlat*Nspin*Norb,Nlat*Nspin*Norb) :: invg_lso,invg0_lso,sigma,Gk_lso
!
out_1=0.d0
!
g=zero
invg0=zero
invg_lso=zero
invg0_lso=zero
Gk_lso=zero
Sigma=zero
!
!
call ed_gf_cluster(omega,g)
invg_lso=nnn2lso_reshape(g,Nlat,Nspin,Norb)
call inv(invg_lso)
invg0=invg0_bath(omega)
invg0_lso=nnn2lso_reshape(invg0,Nlat,Nspin,Norb)
Sigma=invg0_lso-invg_lso
!
do ii=1,size(Hk,3)
Gk_lso=(xi*omega+xmu)*eye(Nlat*Nspin*Norb) - Hk(:,:,ii)- Sigma
call inv(Gk_lso)
out_1=out_1+DREAL(trace(matmul(sij(:,:,ii),Gk_lso)))
enddo
out_1=out_1/(size(Hk,3))
!
return
!
end function sum_observable_kmesh_complex
!+-------------------------------------------------------------------+
!PURPOSE : Get internal energy from the Impurity problem.
!+-------------------------------------------------------------------+
subroutine lanc_local_energy()
integer :: istate,iud(2),jud(2),is,js
integer,dimension(2*Ns_Ud) :: Indices,Jndices
integer,dimension(Ns_Ud) :: iDimUps,iDimDws
integer,dimension(Ns_Ud,Ns_Orb) :: Nups,Ndws ![1,Ns]-[Norb,1+Nbath]
real(8),dimension(Ns) :: Nup,Ndw
type(sector_map),dimension(2*Ns_Ud) :: H
!
Egs = state_list%emin
ed_Ehartree= 0.d0
ed_Eknot = 0.d0
ed_Epot = 0.d0
ed_Dust = 0.d0
ed_Dund = 0.d0
ed_Dse = 0.d0
ed_Dph = 0.d0
!
!
do istate=1,state_list%size
isector = es_return_sector(state_list,istate)
Ei = es_return_energy(state_list,istate)
#ifdef _MPI
if(MpiStatus)then
state_cvec => es_return_cvector(MpiComm,state_list,istate)
else
state_cvec => es_return_cvector(state_list,istate)
endif
#else
state_cvec => es_return_cvector(state_list,istate)
#endif
!
iDim = getdim(isector)
call get_DimUp(isector,iDimUps)
call get_DimDw(isector,iDimDws)
iDimUp = product(iDimUps)
iDimDw = product(iDimDws)
!
peso = 1.d0 ; if(finiteT)peso=exp(-beta*(Ei-Egs))
peso = peso/zeta_function
!
!Master:
if(MpiMaster)then
call build_sector(isector,H)
do i=1,iDim
call state2indices(i,[iDimUps,iDimDws],Indices)
do ii=1,Ns_Ud
mup = H(ii)%map(Indices(ii))
mdw = H(ii+Ns_Ud)%map(Indices(ii+Ns_ud))
Nups(ii,:) = Bdecomp(mup,Ns_Orb) ![Norb,1+Nbath]
Ndws(ii,:) = Bdecomp(mdw,Ns_Orb)
enddo
Nup = Breorder(Nups)
Ndw = Breorder(Ndws)
!
gs_weight=peso*abs(state_cvec(i))**2
!
!> H_Imp: Diagonal Elements, i.e. local part
do ilat=1,Nlat
do iorb=1,Norb
is = imp_state_index(ilat,iorb)
ed_Eknot = ed_Eknot + impHloc(ilat,ilat,1,1,iorb,iorb)*Nup(is)*gs_weight
ed_Eknot = ed_Eknot + impHloc(ilat,ilat,Nspin,Nspin,iorb,iorb)*Ndw(is)*gs_weight
enddo
enddo
! !> H_imp: Off-diagonal elements, i.e. non-local part.
iup = Indices(1) ; idw = Indices(2)
mup = H(1)%map(iup) ; mdw = H(2)%map(idw)
do ilat=1,Nlat
do jlat=1,Nlat
do iorb=1,Norb
do jorb=1,Norb
is = imp_state_index(ilat,iorb)
js = imp_state_index(jlat,jorb)
!UP
Jcondition = &
(impHloc(ilat,jlat,1,1,iorb,jorb)/=0d0) .AND. &
(Nup(js)==1) .AND. (Nup(is)==0)
if (Jcondition) then
call c(js,mup,k1,sg1)
call cdg(is,k1,k2,sg2)
jup = binary_search(H(1)%map,k2)
j = jup + (idw-1)*iDimUp
ed_Eknot = ed_Eknot + &
impHloc(ilat,jlat,1,1,iorb,jorb)*sg1*sg2*state_cvec(i)*(state_cvec(j))
endif
!
!DW
Jcondition = &
(impHloc(ilat,jlat,Nspin,Nspin,iorb,jorb)/=0d0) .AND. &
(ndw(js)==1) .AND. (ndw(is)==0)
if (Jcondition) then
call c(js,mdw,k1,sg1)
call cdg(is,k1,k2,sg2)
jdw = binary_search(H(2)%map,k2)
j = iup + (jdw-1)*iDimUp
ed_Eknot = ed_Eknot + &
impHloc(ilat,jlat,Nspin,Nspin,iorb,jorb)*sg1*sg2*state_cvec(i)*(state_cvec(j))
endif
enddo
enddo
enddo
enddo
!
!
!DENSITY-DENSITY INTERACTION: SAME ORBITAL, OPPOSITE SPINS
!Euloc=\sum=i U_i*(n_u*n_d)_i
!ed_Epot = ed_Epot + dot_product(uloc,nup*ndw)*gs_weight
do ilat=1,Nlat
do iorb=1,Norb
is = imp_state_index(ilat,iorb)
ed_Epot = ed_Epot + Uloc(iorb)*nup(is)*ndw(is)*gs_weight
enddo
enddo
!
!DENSITY-DENSITY INTERACTION: DIFFERENT ORBITALS, OPPOSITE SPINS
!Eust=\sum_ij Ust*(n_up_i*n_dn_j + n_up_j*n_dn_i)
! "="\sum_ij (Uloc - 2*Jh)*(n_up_i*n_dn_j + n_up_j*n_dn_i)
if(Norb>1)then
do ilat=1,Nlat
do iorb=1,Norb
do jorb=iorb+1,Norb
is = imp_state_index(ilat,iorb)
js = imp_state_index(ilat,jorb)
ed_Epot = ed_Epot + Ust*(nup(is)*ndw(js) + nup(js)*ndw(is))*gs_weight
ed_Dust = ed_Dust + (nup(is)*ndw(js) + nup(js)*ndw(is))*gs_weight
enddo
enddo
enddo
endif
!
!DENSITY-DENSITY INTERACTION: DIFFERENT ORBITALS, PARALLEL SPINS
!Eund = \sum_ij Und*(n_up_i*n_up_j + n_dn_i*n_dn_j)
! "="\sum_ij (Ust-Jh)*(n_up_i*n_up_j + n_dn_i*n_dn_j)
! "="\sum_ij (Uloc-3*Jh)*(n_up_i*n_up_j + n_dn_i*n_dn_j)
if(Norb>1)then
do ilat=1,Nlat
do iorb=1,Norb
do jorb=iorb+1,Norb
is = imp_state_index(ilat,iorb)
js = imp_state_index(ilat,jorb)
ed_Epot = ed_Epot + (Ust-Jh)*(nup(is)*nup(js) + ndw(is)*ndw(js))*gs_weight
ed_Dund = ed_Dund + (nup(is)*nup(js) + ndw(is)*ndw(js))*gs_weight
enddo
enddo
enddo
endif
!
!HARTREE-TERMS CONTRIBUTION:
if(hfmode)then
!ed_Ehartree=ed_Ehartree - 0.5d0*dot_product(uloc,nup+ndw)*gs_weight + 0.25d0*sum(uloc)*gs_weight
do ilat=1,Nlat
do iorb=1,Norb
is =imp_state_index(ilat,iorb)
ed_Ehartree=ed_Ehartree - 0.5d0*uloc(iorb)*(nup(is)+ndw(is))*gs_weight + 0.25d0*uloc(is)*gs_weight
enddo
enddo
if(Norb>1)then
do ilat=1,Nlat
do iorb=1,Norb
do jorb=iorb+1,Norb
is=imp_state_index(ilat,iorb)
js=imp_state_index(ilat,jorb)
ed_Ehartree=ed_Ehartree - 0.5d0*Ust*(nup(is)+ndw(is)+nup(js)+ndw(js))*gs_weight + 0.25d0*Ust*gs_weight
ed_Ehartree=ed_Ehartree - 0.5d0*(Ust-Jh)*(nup(is)+ndw(is)+nup(js)+ndw(js))*gs_weight + 0.25d0*(Ust-Jh)*gs_weight
enddo
enddo
enddo
endif
endif
enddo
call delete_sector(isector,H)
endif
!
#ifdef _MPI
if(MpiStatus)then
if(associated(state_cvec))deallocate(state_cvec)
else
if(associated(state_cvec))nullify(state_cvec)
endif
#else
if(associated(state_cvec))nullify(state_cvec)
#endif
!
enddo
!
!
#ifdef _MPI
if(MpiStatus)then
call Bcast_MPI(MpiComm,ed_Epot)
call Bcast_MPI(MpiComm,ed_Eknot)
call Bcast_MPI(MpiComm,ed_Ehartree)
call Bcast_MPI(MpiComm,ed_Dust)
call Bcast_MPI(MpiComm,ed_Dund)
endif
#endif
!
ed_Epot = ed_Epot + ed_Ehartree
!
if(ed_verbose==3)then
write(LOGfile,"(A,10f18.12)")"<Hint> =",ed_Epot
write(LOGfile,"(A,10f18.12)")"<V> =",ed_Epot-ed_Ehartree
write(LOGfile,"(A,10f18.12)")"<E0> =",ed_Eknot
write(LOGfile,"(A,10f18.12)")"<Ehf> =",ed_Ehartree
write(LOGfile,"(A,10f18.12)")"Dust =",ed_Dust
write(LOGfile,"(A,10f18.12)")"Dund =",ed_Dund
endif
!
if(MPIMASTER)then
call write_energy_info()
call write_energy()
endif
!
!
end subroutine lanc_local_energy
!####################################################################
! COMPUTATIONAL ROUTINES
!####################################################################
!+-------------------------------------------------------------------+
!PURPOSE : get scattering rate and renormalization constant Z
!+-------------------------------------------------------------------+
subroutine get_szr()
integer :: ilat,ispin,iorb
real(8) :: wm1,wm2
wm1 = pi/beta ; wm2=3d0*pi/beta
do ilat=1,Nlat
do ispin=1,Nspin
do iorb=1,Norb
simp(ilat,iorb,ispin) = dimag(impSmats(ilat,ilat,ispin,ispin,iorb,iorb,1)) - &
wm1*(dimag(impSmats(ilat,ilat,ispin,ispin,iorb,iorb,2))-dimag(impSmats(ilat,ilat,ispin,ispin,iorb,iorb,1)))/(wm2-wm1)
zimp(ilat,iorb,ispin) = 1.d0/( 1.d0 + abs( dimag(impSmats(ilat,ilat,ispin,ispin,iorb,iorb,1))/wm1 ))
enddo
enddo
enddo
end subroutine get_szr
!+-------------------------------------------------------------------+
!PURPOSE : write legend, i.e. info about columns
!+-------------------------------------------------------------------+
subroutine write_legend()
integer :: unit,iorb,jorb,ispin
unit = free_unit()
open(unit,file="observables_info.ed")
write(unit,"(A1,90(A10,6X))")"#",&
(reg(txtfy(iorb))//"dens_"//reg(txtfy(iorb)),iorb=1,Norb),&
(reg(txtfy(Norb+iorb))//"docc_"//reg(txtfy(iorb)),iorb=1,Norb),&
(reg(txtfy(2*Norb+iorb))//"nup_"//reg(txtfy(iorb)),iorb=1,Norb),&
(reg(txtfy(3*Norb+iorb))//"ndw_"//reg(txtfy(iorb)),iorb=1,Norb),&
(reg(txtfy(4*Norb+iorb))//"mag_"//reg(txtfy(iorb)),iorb=1,Norb),&
reg(txtfy(5*Norb+1))//"s2",&
reg(txtfy(5*Norb+2))//"egs",&
((reg(txtfy(5*Norb+3+(ispin-1)*Norb+iorb))//"z_"//reg(txtfy(iorb))//"s"//reg(txtfy(ispin)),iorb=1,Norb),ispin=1,Nspin),&
((reg(txtfy((5+Nspin)*Norb+3+(ispin-1)*Norb+iorb))//"sig_"//reg(txtfy(iorb))//"s"//reg(txtfy(ispin)),iorb=1,Norb),ispin=1,Nspin)
close(unit)
!
unit = free_unit()
open(unit,file="parameters_info.ed")
write(unit,"(A1,90(A14,1X))")"#","1xmu","2beta",&
(reg(txtfy(2+iorb))//"U_"//reg(txtfy(iorb)),iorb=1,Norb),&
reg(txtfy(2+Norb+1))//"U'",reg(txtfy(2+Norb+2))//"Jh"
close(unit)
!
iolegend=.false.
end subroutine write_legend
subroutine write_custom_legend()
integer :: unit,i
unit = free_unit()
open(unit,file="custom_observables_info.ed")
write(unit,"(A1,90(A10,6X))")"#",(reg(txtfy(i))//reg(custom_o%item(i)%o_name),i=1,custom_o%N_filled)
close(unit)
end subroutine write_custom_legend
subroutine write_energy_info()
integer :: unit
unit = free_unit()
open(unit,file="energy_info.ed")
write(unit,"(A1,90(A14,1X))")"#",&
reg(txtfy(1))//"<Hi>",&
reg(txtfy(2))//"<V>=<Hi-Ehf>",&
reg(txtfy(3))//"<Eloc>",&
reg(txtfy(4))//"<Ehf>",&
reg(txtfy(5))//"<Dst>",&
reg(txtfy(6))//"<Dnd>"
close(unit)
end subroutine write_energy_info
!+-------------------------------------------------------------------+
!PURPOSE : write observables to file
!+-------------------------------------------------------------------+
subroutine write_observables()
integer :: unit
integer :: iorb,jorb,ispin,ilat
unit = free_unit()
do ilat=1,Nlat
open(unit,file="observables_all"//reg(ed_file_suffix)//"_site"//str(ilat,3)//".ed",position='append')
write(unit,"(90(F15.9,1X))")&
(dens(ilat,iorb),iorb=1,Norb),&
(docc(ilat,iorb),iorb=1,Norb),&
(dens_up(ilat,iorb),iorb=1,Norb),&
(dens_dw(ilat,iorb),iorb=1,Norb),&
(magz(ilat,iorb),iorb=1,Norb),&
s2tot,egs,&
((zimp(ilat,iorb,ispin),iorb=1,Norb),ispin=1,Nspin),&
((simp(ilat,iorb,ispin),iorb=1,Norb),ispin=1,Nspin)
close(unit)
enddo
!
unit = free_unit()
do ilat=1,Nlat
open(unit,file="parameters_last"//reg(ed_file_suffix)//".ed")
write(unit,"(90F15.9)")xmu,beta,(uloc(iorb),iorb=1,Norb),Ust,Jh,Jx,Jp
close(unit)
enddo
!
unit = free_unit()
do ilat=1,Nlat
open(unit,file="observables_last"//reg(ed_file_suffix)//"_site"//str(ilat,3)//".ed")
write(unit,"(90(F15.9,1X))")&
(dens(ilat,iorb),iorb=1,Norb),&
(docc(ilat,iorb),iorb=1,Norb),&
(dens_up(ilat,iorb),iorb=1,Norb),&
(dens_dw(ilat,iorb),iorb=1,Norb),&
(magz(ilat,iorb),iorb=1,Norb),&
s2tot,egs,&
((zimp(ilat,iorb,ispin),iorb=1,Norb),ispin=1,Nspin),&
((simp(ilat,iorb,ispin),iorb=1,Norb),ispin=1,Nspin)
close(unit)
enddo
unit = free_unit()
open(unit,file="Sz_ij_ab_last"//reg(ed_file_suffix)//".ed")
write(unit,"(A)")"#I, J, a, b, Sz(I,J,a,b)"
do ilat=1,Nlat
do jlat=1,Nlat
do iorb=1,Norb
do jorb=1,Norb
write(unit,"(4I15,F15.9)")ilat,jlat,iorb,jorb,sz2(ilat,jlat,iorb,jorb)
enddo
enddo
enddo
enddo
close(unit)
open(unit,file="N2_ij_ab_last"//reg(ed_file_suffix)//".ed")
write(unit,"(A)")"#I, J, a, b, N2(I,J,a,b)"
do ilat=1,Nlat
do jlat=1,Nlat
do iorb=1,Norb
do jorb=1,Norb
write(unit,"(4I15,F15.9)")ilat,jlat,iorb,jorb,n2(ilat,jlat,iorb,jorb)
enddo
enddo
enddo
enddo
close(unit)
end subroutine write_observables
subroutine write_custom_observables()
integer :: i
integer :: unit
unit = free_unit()
open(unit,file="custom_observables_all.ed",position='append')
write(unit,"(90(F15.9,1X))")&
(custom_o%item(i)%o_value,i=1,custom_o%N_filled)
close(unit)
!
unit = free_unit()
open(unit,file="custom_observables_last.ed")
write(unit,"(90(F15.9,1X))")&
(custom_o%item(i)%o_value,i=1,custom_o%N_filled)
close(unit)
!
end subroutine write_custom_observables
subroutine write_energy()
integer :: unit
unit = free_unit()
open(unit,file="energy_last"//reg(ed_file_suffix)//".ed")
write(unit,"(90F15.9)")ed_Epot,ed_Epot-ed_Ehartree,ed_Eknot,ed_Ehartree,ed_Dust,ed_Dund!,ed_Dse,ed_Dph
close(unit)
end subroutine write_energy
END MODULE ED_OBSERVABLES