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bhz_2d_mf_fluct.f90
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bhz_2d_mf_fluct.f90
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program bhz_2d
!LIBRARIES:
USE SCIFOR
USE DMFT_TOOLS
!
USE MPI
implicit none
!
!SET THE DIMENSION OF THE PROBLEM
integer,parameter :: Norb=2
integer,parameter :: Nspin=2
integer,parameter :: Nso=Nspin*Norb
!
!INPUT VARIABLES
integer :: Nkx,Nky,Nktot
integer :: L,Lf,Lb
integer :: Iter
integer :: MaxIter
integer :: Nsuccess=0
integer :: OrderInt
real(8) :: gt
real(8) :: gn
real(8) :: mh
real(8) :: lambda
real(8) :: xmu
real(8) :: beta
real(8) :: eps
real(8) :: wmix
real(8) :: it_error
real(8) :: tz0
real(8) :: dtz0
real(8) :: dplus0,dminus0
logical :: withgf,check_nel
!
!Gamma matrices:
complex(8),dimension(Nso,Nso) :: Gamma1,Gamma2,Gamma5,GammaN
!
!GLOBALLY SHARED VARIABLES:
real(8) :: Tz !the orbital polarization
real(8) :: Ne !the total density
real(8),dimension(:,:),allocatable :: kgrid !K vector grid
!
!WORK ARRAYS:
real(8),dimension(:),allocatable :: p_work
real(8) :: qvec_work(2)
integer :: m_work
!
integer :: Nparams
integer :: i,j,k,ik,m,n
integer :: info,unit
real(8) :: x(1),dx(1),ran(10)
logical :: iexist
logical :: converged
complex(8),dimension(:,:,:),allocatable :: Hk
complex(8),dimension(:,:,:,:,:),allocatable :: Smats
complex(8),dimension(:,:,:,:,:),allocatable :: Gmats
character(len=20) :: Finput
real(8),dimension(:),allocatable :: params
real(8),dimension(:),allocatable :: params_prev
real(8),dimension(2,2) :: Chi_qv,Chi
!MPI Vars:
integer :: comm,ierr,mpiId,mpiSize
logical :: master
call init_MPI()
comm = MPI_COMM_WORLD
call StartMsg_MPI(comm)
mpiId = get_Rank_MPI(comm)
mpiSize= get_Size_MPI(comm)
master = get_Master_MPI(comm)
call parse_cmd_variable(Finput,"FINPUT",default="input.conf")
call parse_input_variable(gt,"GT",Finput,default=1d0)
call parse_input_variable(gn,"GN",Finput,default=1d0)
call parse_input_variable(nkx,"NKX",Finput,default=10)
call parse_input_variable(Lf,"LF",Finput,default=256,comment="# of fermionic Mats frequencies, L=Lf+Lb")
call parse_input_variable(Lb,"LB",Finput,default=64,comment="# of bosonix Mats frequencies, L=Lf+Lb")
call parse_input_variable(Mh,"MH",Finput,default=1d0)
call parse_input_variable(lambda,"LAMBDA",Finput,default=0.3d0)
call parse_input_variable(xmu,"XMU",Finput,default=0.d0)
call parse_input_variable(beta,"BETA",Finput,default=1000.d0)
call parse_input_variable(tz0,"tz0",Finput,default=-0.1d0,comment="Guess for MF search of Tz (tz0<0)")
call parse_input_variable(dtz0,"dtz0",Finput,default=0.1d0,comment="Guess for dTz fluctuations (dtz0>0)")
call parse_input_variable(dplus0,"dplus0",Finput,default=0.1d0,comment="Guess for d+0 fluctuations (d+0>0)")
call parse_input_variable(dminus0,"dminus0",Finput,default=0.1d0,comment="Guess for d-0 fluctuations (d-0>0)")
call parse_input_variable(it_error,"IT_ERROR",Finput,default=1d-5)
call parse_input_variable(maxiter,"MAXITER",Finput,default=100)
call parse_input_variable(eps,"EPS",Finput,default=4.d-2)
call parse_input_variable(wmix,"WMIX",Finput,default=1d0)
call parse_input_variable(withgf,"WITHGF",Finput,default=.false.)
call parse_input_variable(check_nel,"check_nel",Finput,default=.false.)
call parse_input_variable(OrderInt,"ORDERINT",Finput,default=0)
call print_input(trim(Finput))
call save_input_file(trim(Finput))
!
call add_ctrl_var(beta,"BETA")
call add_ctrl_var(Norb,"NORB")
call add_ctrl_var(Nspin,"Nspin")
call add_ctrl_var(xmu,"xmu")
call add_ctrl_var(-10d0,"wini")
call add_ctrl_var(10d0,"wfin")
call add_ctrl_var(eps,"eps")
if(gn==0d0.OR.gt==0d0)stop "ERROR: gt AND gn should be non zero (check in progress)"
gamma1 = kron_pauli( pauli_sigma_z, pauli_tau_x)
gamma2 = kron_pauli( pauli_sigma_0,-pauli_tau_y)
gamma5 = kron_pauli( pauli_sigma_0, pauli_tau_z)
gammaN = kron_pauli( pauli_sigma_0, pauli_tau_0)
Nky = Nkx
Nktot = Nkx*Nky
!
L = Lf+Lb
if(master)write(*,*)"Using L freq.=",L
!>SOLVE MF PROBLEM 1st: >>ACTHUNG<< This solution does not use BZ basis defined later!!
if(master)call start_timer()
x(1)=-abs(tz0)
dx(1)=0.1d0
call fmin(bhz_f,x,lambda=dx)
Tz=x(1)
if(master)then
open(free_unit(unit),file="mf_TzVSg.dat")
write(unit,*)gt,gn,Tz
close(unit)
write(*,*) "Tz=",Tz
call stop_timer(" Mean-Field")
endif
!> SOLVE FLUCTUATIONS:
!Setup the k-space lattice basis:
call TB_set_bk([pi2,0d0],[0d0,pi2])
allocate(kgrid(Nktot,2)) !Nktot=# tot kpoints, 2= 2D
call TB_build_kgrid([Nkx,Nky],kgrid)
!+ ReSigma(iw_n)[L] + ImSigma(iw_n)[L] + Tz[1] + <|d+|**2>[1]
Nparams = 2 + 2*L
allocate( params(Nparams), params_prev(Nparams), p_work(Nparams))
!Start from MF solution
params = [dble(zeros(L)),dble(zeros(L)),Tz,abs(dplus0)]
if(master)then
inquire(file="params.restart",exist=iexist)
if(iexist)call read_array("params.restart",params)
call save_array("params.init",params)
endif
call bcast_MPI(comm,params)
if(master)then
open(free_unit(unit),file="chi0_q0.dat ")
p_work = params
qvec_work= [0d0,0d0]
do m=-Lb,Lb
call Intk_SumMats_Chi_qv(m,Chi_qv)
write(unit,*)2d0*pi*m/beta, Chi_qv(1,1),Chi_qv(2,2),Chi_qv(1,2)
end do
close(unit)
endif
converged=.false. ; iter=0
do while(.not.converged.AND.iter<maxiter)
iter=iter+1
call start_loop(iter,maxiter,"SC-loop")
!
!>SOLVE 4 EQUATIONS For Delta,<|dDelta|**2>,Sigma
call solve_eqs(params)
if(iter>1)params = wmix*params + (1d0-wmix)*params_prev
params_prev = params
!
converged = check_convergence_local(params,it_error,nsuccess,maxiter)
if(master)then
call save_array("params.iter"//str(iter,4),params)
open(free_unit(unit),file="tz_dtz_all.dat",access='append')
write(unit,*)iter,params(2*L+1),params(2*L+2)
close(unit)
endif
call end_loop
end do
call save_array("params.restart",params)
!
if(master)then
open(free_unit(unit),file="tz_dtzVSg.dat")
write(unit,*)gt,gn,params(2*L+1),params(2*L+2)
close(unit)
write(*,*) "Tz, d+=",params(2*L+1),params(2*L+2)
endif
allocate(Smats(Nspin,Nspin,Norb,Norb,L))
allocate(Gmats(Nspin,Nspin,Norb,Norb,L))
allocate(Hk(Nso,Nso,Nktot));Hk=zero
!
call TB_build_model(Hk,hk_bhz,Nso,[Nkx,Nky])
call build_self_energy(params,Smats)
call dmft_gloc_matsubara(Hk,Gmats,Smats)
call dmft_print_gf_matsubara(Smats,"Smats",iprint=1)
call dmft_print_gf_matsubara(Gmats,"Gloc",iprint=1)
if(master)then
open(free_unit(unit),file="chi_q0.dat ")
p_work = params
Chi = 0d0
do m=-Lb,Lb
qvec_work=[0d0,0d0]
call Intk_SumMats_Chi_qv(m,Chi_qv)
write(unit,*) 2d0*pi*m/beta, Chi_qv(1,1),Chi_qv(2,2),Chi_qv(1,2)
enddo
close(unit)
if(check_nel)then
do ik=1,Nktot
qvec_work=Kgrid(ik,:)
do m=-Lb,Lb
call Intk_SumMats_Chi_qv(m,Chi_qv)
Chi = Chi + Chi_qv/Nktot/beta
enddo
end do
write(*,*)Chi(1,1),Chi(2,2),Chi(1,2)
endif
endif
call finalize_MPI()
contains
!For MF calculations:
!#################################
function bhz_f(a) result(f)
real(8),dimension(:) :: a
real(8) :: f
real(8) :: integral
Tz = a(1)
call gauss_quad(Fmf_bhz,[0d0,0d0],[pi2,pi2],integral)
f = gt*(Tz**2) - 2d0*integral/pi2/pi2
end function bhz_f
function Fmf_bhz(kvec) result(Fk)
real(8),dimension(:) :: kvec
real(8) :: Fk
real(8) :: ek,x2,y2,kx,ky
kx = kvec(1)
ky = kvec(2)
ek = -1d0*(cos(kx)+cos(ky))
x2 = lambda*sin(kx) ;x2=x2**2
y2 = lambda*sin(ky) ;y2=y2**2
Fk = sqrt( (mh - gt*Tz + ek)**2 + (x2+y2) )
end function fmf_bhz
!#################################
subroutine solve_eqs(p)
real(8),dimension(:),intent(inout) :: p ![3+2L]
real(8),dimension(Nparams) :: integral,ints
real(8) :: Tz,dTz
real(8) :: TzTmp,dPlus
real(8),dimension(L) :: ReSigma,ImSigma
real(8) :: N_el
complex(8) :: Smats(Nspin,Nspin,Norb,Norb,L)
complex(8) :: Gkmats(Nso,Nso,L)
real(8) :: n_k(Nktot,Nso),kvec(2)
!
p_work = p
!
select case(OrderInt)
case default
integral = 0d0
do ik=1,Nktot
kvec = Kgrid(ik,:)
integral = integral + fk_system(kvec,Nparams)/Nktot
enddo
case(1)
integral = trapz2d_system(Nparams,fk_system,[0d0,pi2],[0d0,pi2],Nkx,Nkx)/pi2/pi2
end select
!
resigma = integral(1:L)
ImSigma = integral(L+1:2*L)
Tz = integral(2*L+1)
dPlus = integral(2*L+2)
!
!Update params:
p(1:L) = ReSigma
p(L+1:2*L) = ImSigma
p(2*L+1) = Tz
p(2*L+2) = dPlus
!
if(check_nel)then
call build_self_energy(p,Smats)
do ik=1,Nktot
kvec = Kgrid(ik,:)
do i=1,L
Gkmats(:,:,i) = get_simplified_gf(kvec,i,Nso,so2j(Smats(:,:,:,:,i)))
end do
do i=1,Nso
n_k(ik,i) = fft_get_density(Gkmats(i,i,:),beta)
end do
end do
N_el = sum(n_k)/Nktot
if(master)write(*,*)"N=",N_el
if(master)call splot("Sigma_iw_iter"//str(iter,3)//".dat",pi/beta*(2*arange(1,L)-1),dcmplx(ReSigma(:),ImSigma(:)))
endif
if(master)write(*,*)"Tz =",Tz
if(master)write(*,*)"D+ =",dPlus
if(master)write(*,*)"ReS(1), ImS(1) =",ReSigma(1),ImSigma(1)
return
end subroutine solve_eqs
function fk_system(kvec,dim) result(integral)
real(8),dimension(:) :: kvec
integer :: dim
real(8),dimension(dim) :: integral
!
integer :: n,m,ik,iq
real(8) :: kx,ky
real(8),dimension(L) :: ReSigma,ImSigma
real(8),dimension(L) :: ReSTmp,ImSTmp
real(8),dimension(L) :: ReS,ImS
real(8) :: Tz,dTz,dPlus
real(8) :: TzTmp,dTzTmp,dPlusTmp
real(8) :: z,simZ
real(8) :: Ek,simEk
real(8) :: Meff
real(8) :: xk,yk
real(8) :: Den,gplus,gminus
real(8) :: ChiTmp(2,2)
!
if(dim/=Nparams)stop "f_system ERROR: Dim != Nparams"
!
!split params as required:
ReSigma = p_work(1:L)
ImSigma = p_work(L+1:2*L)
Tz = p_work(2*L+1)
dPlus = p_work(2*L+2)
qvec_work = kvec !q==k
!
kx = kvec(1)
ky = kvec(2)
ek = -1d0*(cos(kx)+cos(ky))
xk = lambda*sin(kx)
yk = lambda*sin(ky)
!
gplus = 1d0/gt + 1d0/gn
gminus = -1d0/gt + 1d0/gn
!
!Sum over Matsubara frequencies first:
ReS = 0d0
ImS = 0d0
!
ReSTmp = 0d0
ImSTmp = 0d0
TzTmp = 0d0
dPlusTmp = 0d0
do n=1+mpiId,L,mpiSize
z = pi/beta*(2*n-1)
simZ = z - ImSigma(n) !modulo a factor xi
Meff = Mh - Tz*gt + ek + ReSigma(n)
simEk = Meff**2 + xk**2 + yk**2
Den = z**2 + simEk
TzTmp = TzTmp - 2d0*Meff/Den !Sum over n
ReSTmp(n) = -Meff/Den*dPlus
ImSTmp(n) = -simZ/Den*dPlus
if(n==1.AND.kx==0.AND.ky==0)print*,ImSTmp(n),SimZ/Den,dPlus,Meff,Mh - Tz*gt + ek,ReSTmp(n)
enddo
call AllReduce_MPI(comm,ReSTmp,ReS)
call AllReduce_MPI(comm,ImSTmp,ImS)
Tz = 0d0
call AllReduce_MPI(comm,TzTmp,Tz)
!
!Int(k) Chi({q,m};k) = Int(k)Sum(n) Chi({q,m};{k,n})
do n=0+mpiId,2*Lb,mpiSize
m = -Lb + n !m=-Lb,Lb
call Intk_SumMats_Chi_qv(m,ChiTmp)
Den = (ChiTmp(1,1) + gminus)**2 - ChiTmp(1,2)**2 - (ChiTmp(2,2) + gplus)**2
dPlusTmp = dPlusTmp -2d0*(ChiTmp(1,1) + gminus)/Den - (gt-gn)/2d0
enddo
dPlus = 0d0
call AllReduce_MPI(comm,dPlusTmp,dPlus)
!
integral(1:L) = ReS !ReSigma(k)
integral(L+1:2*L) = ImS !ImSigma(k)
integral(2*L+1) = 2d0*Tz/beta !Tz(k)
integral(2*L+2) = dPlus/beta !d+(q)
end function fk_system
subroutine Intk_SumMats_Chi_qv(m,chi)
integer :: m
real(8) :: chi(2,2)
real(8),dimension(2) :: kvec
real(8) :: Tz,dPlus
real(8),dimension(-L:L) :: ReSigma,ImSigma
real(8) :: wn,wn_plus_m,wn_minus_m
real(8) :: zn,zn_plus_m,zn_minus_m
real(8) :: ek0,ek0_plus_q
real(8) :: xk,xk_plus_q
real(8) :: yk,yk_plus_q
real(8) :: Ek_n, Ek_plus_q__n_plus_m, Ek_plus_q__n_minus_m
real(8) :: Mk_n, Mk_plus_q__n_plus_m, Mk_plus_q__n_minus_m
real(8) :: Dk_n, Dk_plus_q__n_plus_m, Dk_plus_q__n_minus_m
real(8) :: chi_pp_n_plus_m,chi_pp_n_minus_m,chi_pp
real(8) :: chi_mm_n_plus_m,chi_mm_n_minus_m,chi_mm
real(8) :: chi_pm_n_plus_m,chi_pm_n_minus_m,chi_pm
real(8) :: chi_pp_n_plus_m_t,chi_pp_n_minus_m_t,chi_pp_t
real(8) :: chi_mm_n_plus_m_t,chi_mm_n_minus_m_t,chi_mm_t
real(8) :: chi_pm_n_plus_m_t,chi_pm_n_minus_m_t,chi_pm_t
real(8) :: Den_n__n_plus_m,Den_n__n_minus_m
real(8) :: Mk_t, Mkq_t, Ek_t, Ekq_t
real(8) :: tail_num(2,2),tail(2,2),tail_den, nu
integer :: ik,n
real(8) :: kx,ky,qx,qy,vkq,Tfactor,chi_pp_t_sum,chi_mm_t_sum,chi_pm_t_sum
ReSigma(1:L) = p_work(1:L) ; ReSigma(-L:-1)=ReSigma(1:L) ; ReSigma(0) = 0d0
ImSigma(1:L) = p_work(L+1:2*L) ; ImSigma(-L:-1)=-ImSigma(1:L); ImSigma(0) = 0d0
Tz = p_work(2*L+1)
dPlus = p_work(2*L+2)
!
tail_den = 0d0
tail_num = 0d0
Chi = 0d0
qx = qvec_work(1)
qy = qvec_work(2)
nu = 2*m*pi/beta
!
do ik=1,Nktot
kvec = Kgrid(ik,:)
kx = kvec(1)
ky = kvec(2)
!
ek0 = -1d0*(cos(kx)+cos(ky))
ek0_plus_q = -1d0*(cos(kx+qx)+cos(ky+qy))
xk = lambda*sin(kx)
yk = lambda*sin(ky)
xk_plus_q = lambda*sin(kx+qx)
yk_plus_q = lambda*sin(ky+qy)
vkq = xk*xk_plus_q + yk*yk_plus_q
!
Mk_t = Mh - Tz*gt + ek0
Mkq_t = Mh - Tz*gt + ek0_plus_q
!
Ek_t = Mk_t**2 + xk**2 + yk**2
Ekq_t = Mkq_t**2 + xk_plus_q**2 + yk_plus_q**2
!
do n=1,Lf
wn = pi/beta*(2*n-1)
wn_plus_m = pi/beta*(2*(n+m)-1)
wn_minus_m = pi/beta*(2*(n-m)-1)
!
zn = wn - ImSigma(n) !n -->-n
zn_plus_m = wn_plus_m - ImSigma(n+m) !n+m -->-n-m
zn_minus_m = wn_minus_m - ImSigma(n-m) !n-m --> m-n
!
Mk_n = Mh - Tz*gt + ReSigma(n) + ek0
Mk_plus_q__n_plus_m = Mh - Tz*gt + ReSigma(n+m) + ek0_plus_q
Mk_plus_q__n_minus_m = Mh - Tz*gt + ReSigma(n-m) + ek0_plus_q
!
Ek_n = Mk_n**2 + xk**2 + yk**2
Ek_plus_q__n_plus_m = Mk_plus_q__n_plus_m**2 + xk_plus_q**2 + yk_plus_q**2
Ek_plus_q__n_minus_m = Mk_plus_q__n_minus_m**2 + xk_plus_q**2 + yk_plus_q**2
!
Dk_n = zn**2 + Ek_n
Dk_plus_q__n_plus_m = zn_plus_m**2 + Ek_plus_q__n_plus_m
Dk_plus_q__n_minus_m = zn_minus_m**2 + Ek_plus_q__n_minus_m
!
Den_n__n_plus_m = Dk_n*Dk_plus_q__n_plus_m
Den_n__n_minus_m = Dk_n*Dk_plus_q__n_minus_m
!
!
!Chi_++
chi_pp_n_plus_m = (-zn*zn_plus_m + Mk_n*Mk_plus_q__n_plus_m)/Den_n__n_plus_m
chi_pp_n_minus_m = (-zn*zn_minus_m + Mk_n*Mk_plus_q__n_minus_m)/Den_n__n_minus_m
chi_pp = chi_pp_n_plus_m + chi_pp_n_minus_m
Chi(1,1) = Chi(1,1) - 2d0*chi_pp/beta/Nktot
!
chi_pp_n_plus_m_t = (-wn*wn_plus_m + Mkq_t*Mk_t)/(wn**2+Ek_t)/(wn_plus_m**2+Ekq_t)
chi_pp_n_minus_m_t = (-wn*wn_minus_m + Mkq_t*Mk_t)/(wn**2+Ek_t)/(wn_minus_m**2+Ekq_t)
chi_pp_t = chi_pp_n_plus_m_t + chi_pp_n_minus_m_t
Chi(1,1) = Chi(1,1) + 2d0*chi_pp_t/beta/Nktot
!
!
!Chi_--
chi_mm_n_plus_m = vkq/Den_n__n_plus_m
chi_mm_n_minus_m = vkq/Den_n__n_minus_m
chi_mm = chi_mm_n_plus_m + chi_mm_n_minus_m
Chi(2,2) = Chi(2,2) - 2d0*chi_mm/beta/Nktot
!
chi_mm_n_plus_m_t = vkq/(wn**2+Ek_t)/(wn_plus_m**2+Ekq_t)
chi_mm_n_minus_m_t = vkq/(wn**2+Ek_t)/(wn_minus_m**2+Ekq_t)
chi_mm_t = chi_mm_n_plus_m_t + chi_mm_n_minus_m_t
Chi(2,2) = Chi(2,2) + 2d0*chi_mm_t/beta/Nktot
!
!
!Chi_+-
chi_pm_n_plus_m = (zn*Mk_plus_q__n_plus_m + zn_plus_m*Mk_n)/Den_n__n_plus_m
chi_pm_n_minus_m = (zn*Mk_plus_q__n_minus_m + zn_minus_m*Mk_n)/Den_n__n_minus_m
chi_pm = chi_pm_n_plus_m - chi_pm_n_minus_m
Chi(1,2) = Chi(1,2) - 4d0*chi_pm/beta/Nktot
!
! chi_pm_n_plus_m_t = (wn*Mkq_t + wn_plus_m*Mk_t)/(wn**2 +Ek_t)/(wn_plus_m**2 + Ekq_t)
! chi_pm_n_minus_m_t = (wn*Mkq_t + wn_minus_m*Mk_t)/(wn**2+Ek_t)/(wn_minus_m**2 + Ekq_t)
! chi_pm_t = chi_pm_n_plus_m_t - chi_pm_n_minus_m_t
! Chi(1,2) = Chi(1,2) + 4d0*chi_pm_t/beta/Nktot
Chi(2,1) = Chi(1,2)
enddo
!
!
!
Tfactor = 2d0*tanh(0.5d0*beta*sqrt(Ek_t))/sqrt(Ek_t)
eps = abs(Ekq_t-Ek_t)
if(m==0)then
!in this case eps=0 by construction so we have a specific expression
tail(1,1) = Tfactor*((xk**2 + yk**2)/4d0/Ek_t)
tail(2,2) = -Tfactor*(vkq/4d0/Ek_t)
tail(1,2) = 0d0
tail(2,1) = 0d0
!
elseif(m==0.AND.(qx/=0d0.OR.qy/=0))then
if(eps<1d-3)then
!in this case eps can be small, you have to handle it separately
tail(1,1) = -Tfactor*(Ek_t + Mk_t*Mkq_t)*(2d0 - (Ekq_t-Ek_t))
tail(2,2) = -Tfactor*vkq*(2d0 - (Ekq_t-Ek_t))
tail(1,2) = 0d0
tail(2,1) = 0d0
else
!if eps is not small, then use regular expression
tail_num(1,1) = -Tfactor*(Ek_t + Mk_t*Mkq_t)
tail_num(2,2) = -Tfactor*vkq
tail_num(1,2) = 0d0
tail_num(2,1) = 0d0
tail_den = (Ekq_t-Ek_t)
tail = tail_num/tail_den
endif
else
! m and q generic
tail_num(1,1) = Tfactor*((Ek_t-Ekq_t)*(Ek_t + Mk_t*Mkq_t) + (Ek_t - Mk_t*Mkq_t)*nu**2d0)
tail_num(2,2) = Tfactor*(vkq*(Ek_t - Ekq_t - nu**2d0))
tail_num(1,2) = 0d0
tail_num(2,1) = 0d0
tail_den = ((Ekq_t-Ek_t)**2d0 + 2d0*(Ekq_t+Ek_t)*nu**2d0 + nu**4d0)
tail = tail_num/tail_den
endif
Chi = Chi + tail/Nktot
enddo
end subroutine Intk_SumMats_Chi_qv
subroutine build_self_energy(p,Sigma)
real(8),dimension(:) :: p
complex(8),dimension(Nspin,Nspin,Norb,Norb,L) :: Sigma
complex(8),dimension(Nspin*Norb,Nspin*Norb,L) :: Self
do i=1,L
Self(:,:,i) = -gt*p(2*L+1)*Gamma5 + p(i)*Gamma5 + xi*p(L+i)*GammaN
Sigma(:,:,:,:,i) = j2so(Self(:,:,i))
enddo
end subroutine build_self_energy
!#################################
!#################################
!#################################
!#################################
function hk_bhz(kvec,N) result(hk)
integer :: N
real(8),dimension(:) :: kvec
complex(8),dimension(N,N) :: hk
real(8) :: ek,kx,ky
integer :: ii
if(N/=Nso)stop "hk_bhz error: N != Nspin*Norb == 4"
kx=kvec(1)
ky=kvec(2)
ek = -1d0*(cos(kx)+cos(ky))
Hk = (Mh+ek)*Gamma5 + lambda*sin(kx)*Gamma1 + lambda*sin(ky)*Gamma2
end function hk_bhz
function so2j_index(ispin,iorb) result(isporb)
integer :: ispin,iorb
integer :: isporb
if(iorb>Norb)stop "error so2j_index: iorb>Norb"
if(ispin>Nspin)stop "error so2j_index: ispin>Nspin"
isporb=(ispin-1)*Nspin + iorb
end function so2j_index
function so2j(fg) result(g)
complex(8),dimension(Nspin,Nspin,Norb,Norb) :: fg
complex(8),dimension(Nspin*Norb,Nspin*Norb) :: g
integer :: i,j,iorb,jorb,ispin,jspin
do ispin=1,Nspin
do jspin=1,Nspin
do iorb=1,Norb
do jorb=1,Norb
i=so2j_index(ispin,iorb)
j=so2j_index(jspin,jorb)
g(i,j) = fg(ispin,jspin,iorb,jorb)
enddo
enddo
enddo
enddo
end function so2j
function j2so(fg) result(g)
complex(8),dimension(Nspin*Norb,Nspin*Norb) :: fg
complex(8),dimension(Nspin,Nspin,Norb,Norb) :: g
integer :: i,j,iorb,jorb,ispin,jspin
do ispin=1,Nspin
do jspin=1,Nspin
do iorb=1,Norb
do jorb=1,Norb
i=so2j_index(ispin,iorb)
j=so2j_index(jspin,jorb)
g(ispin,jspin,iorb,jorb) = fg(i,j)
enddo
enddo
enddo
enddo
end function j2so
function get_simplified_gf(kvec,i,N,Sigma) result(gk)
real(8),dimension(:) :: kvec
complex(8) :: z
integer :: i,N
complex(8),dimension(N,N) :: gk,sigma
real(8) :: kx,ky
real(8) :: w_,M_,x_,y,Ek
kx = kvec(1)
ky = kvec(2)
!
w_ = pi/beta*(2*i-1) - dimag(sigma(1,1))
M_ = Mh-1d0*(cos(kx)+cos(ky)) + dreal(sigma(1,1))
x_ = lambda*sin(kx)
y = lambda*sin(ky)
!
Ek = M_**2 + x_**2 + y**2
Gk = xi*w_*eye(Nso) + M_*Gamma5 + x_*Gamma1 + y*Gamma2
Gk = Gk/(-w_**2-Ek)
end function get_simplified_gf
function trapz2d_system(m,func,xrange,yrange,Nx,Ny) result(int)
integer :: m
interface
function func(x,m)
real(8),dimension(:) :: x
integer :: m
real(8) :: func(m)
end function func
end interface
real(8),dimension(2) :: xrange,yrange
integer :: Nx,Ny,i,j
real(8) :: xx(Nx),yy(Ny)
real(8) :: hx,hy
real(8) :: int(m)
hx=xrange(2)-xrange(1)
hx=hx/Nx
hy=yrange(2)-yrange(1)
hy=hy/Ny
int=&
func([xrange(1),yrange(1)],m)+&
func([xrange(1),yrange(2)],m)+&
func([xrange(2),yrange(1)],m)+&
func([xrange(2),yrange(2)],m)
xx=linspace(xrange(1),xrange(2),Nx,iend=.false.)
yy=linspace(yrange(1),yrange(2),Ny,iend=.false.)
do i=2,Nx
do j=2,Ny
int=int+4d0*func([xx(i),yy(j)],m)
enddo
enddo
do j=2,Ny
int=int+2d0*( func([xrange(1),yy(j)],m) + func([xrange(2),yy(j)],m) )
enddo
do i=2,Nx
int=int+2d0*( func([xx(i),yrange(1)],m) + func([xx(i),yrange(2)],m) )
enddo
int=int*hx*hy/4d0
end function trapz2d_system
function trapz2d_func(func,xrange,yrange,Nx,Ny) result(int)
interface
function func(x)
real(8),dimension(:) :: x
real(8) :: func
end function func
end interface
real(8),dimension(2) :: xrange,yrange
integer :: Nx,Ny,i,j
real(8) :: xx(Nx),yy(Ny)
real(8) :: hx,hy
real(8) :: int
hx=xrange(2)-xrange(1)
hx=hx/Nx
hy=yrange(2)-yrange(1)
hy=hy/Ny
int=&
func([xrange(1),yrange(1)])+&
func([xrange(1),yrange(2)])+&
func([xrange(2),yrange(1)])+&
func([xrange(2),yrange(2)])
xx=linspace(xrange(1),xrange(2),Nx,iend=.false.)
yy=linspace(yrange(1),yrange(2),Ny,iend=.false.)
do i=2,Nx
do j=2,Ny
int=int+4d0*func([xx(i),yy(j)])
enddo
enddo
do j=2,Ny
int=int+2d0*( func([xrange(1),yy(j)]) + func([xrange(2),yy(j)]) )
enddo
do i=2,Nx
int=int+2d0*( func([xx(i),yrange(1)]) + func([xx(i),yrange(2)]) )
enddo
int=int*hx*hy/4d0
end function trapz2d_func
end program bhz_2d
! subroutine solve_eqs(p)
! real(8),dimension(:),intent(inout) :: p ![2+2L]
! real(8) :: Tz,dTz,TzTmp,dTzTmp
! real(8),dimension(L) :: ReSigma,ImSigma
! real(8) :: kvec(2),qvec(2)
! real(8) :: wn
! real(8) :: ReS(L),ImS(L)
! real(8) :: Meff,ek,xk,yk,SimEk
! real(8) :: Den,ChiTmp
! complex(8) :: N_el
! complex(8) :: Smats(Nspin,Nspin,Norb,Norb,L)
! complex(8) :: Gkmats(Nso,Nso,L)
! real(8) :: n_k(Nktot,Nso)
! integer :: ik,n,m
! !split params as required:
! ReSigma = p(1:L)
! ImSigma = p(L+1:2*L)
! Tz = p(2*L+1)
! dTz = p(2*L+2)
! !
! ReS = 0d0
! ImS = 0d0
! TzTmp = 0d0
! dTzTmp = 0d0
! !
! do ik=1,Nktot
! kvec = Kgrid(ik,:)
! qvec = Kgrid(ik,:)
! ek = -1d0*(cos(kvec(1))+cos(kvec(2)))
! xk = lambda*sin(kvec(1))
! yk = lambda*sin(kvec(2))
! !
! do n=1,L
! wn = pi/beta*(2*n-1)-ImSigma(n)
! Meff = Mh - Tz*gt + ReSigma(n)
! simEk = (Meff + ek)**2 + xk**2 + yk**2
! Den = wn**2d0 + simEk
! ReS(n) = ReS(n) + (Meff + ek)/Den
! ImS(n) = ImS(n) + wn/Den
! TzTmp = TzTmp + (Meff + ek)/Den
! enddo
! !
! do m=1,Lb
! ChiTmp = Chi_qv(p,qvec,m)
! dTzTmp = dTzTmp + ChiTmp/(1d0-gt*ChiTmp)
! enddo
! enddo
! !
! ReSigma = -ReS*dTz/Nktot
! ImSigma = -ImS*dTz/Nktot
! Tz = -4d0*TzTmp/beta/Nktot
! dTz = 2d0*dTzTmp*gt**2d0/beta/Nktot
! !
! !Update params:
! p(1:L) = ReSigma
! p(L+1:2*L) = ImSigma
! p(2*L+1) = Tz
! p(2*L+2) = dTz
! call build_self_energy(p,Smats)
! do ik=1,Nktot
! kvec = Kgrid(ik,:)
! do i=1,L
! Gkmats(:,:,i) = get_simplified_gf(kvec,i,Nso,so2j(Smats(:,:,:,:,i)))
! end do
! do i=1,Nso
! n_k(ik,i) = fft_get_density(Gkmats(i,i,:),beta)
! end do
! end do
! N_el = sum(n_k)/Nktot
! write(*,*)iter,Tz,dTz,ReSigma(1),ImSigma(1), N_el
! call splot("Sigma_iw_iter"//str(iter,3)//".dat",pi/beta*(2*arange(1,L)-1),dcmplx(ReSigma(:),ImSigma(:)))
! return
! end subroutine solve_eqs
! function Chi_qv(p,qvec,m) result(chi)
! real(8),dimension(:),intent(in) :: p
! real(8),dimension(:),intent(in) :: qvec
! integer,intent(in) :: m
! real(8) :: chi
! real(8) :: Tz,dTz
! real(8),dimension(L) :: ReSigma,ImSigma
! real(8) :: kvec(2)
! real(8) :: wn,wn_plus_m
! real(8) :: Mk,Mk_plus_q
! real(8) :: ek,ek_plus_q
! real(8) :: xk,xk_plus_q
! real(8) :: yk,yk_plus_q
! real(8) :: SimEk,SimEk_plus_q
! real(8) :: Dk,Dk_plus_q
! real(8) :: num,den
! real(8) :: num_t,den_t, Mk_t, Mkq_t, Ek2, Ekq2
! real(8) :: tail_num, tail_den, tail, nu
! integer :: ik,n
! real(8) :: kx,ky,qx,qy,vkq
! ReSigma = p(1:L)
! ImSigma = p(L+1:2*L)
! Tz = p(2*L+1)
! dTz = p(2*L+2)
! Chi = 0d0
! tail = 0d0
! qx = qvec(1)
! qy = qvec(2)
! nu = 2*m*pi/beta
! do ik=1,Nktot
! kx = Kgrid(ik,1)
! ky = Kgrid(ik,2)
! ek = -1d0*(cos(kx)+cos(ky))
! ek_plus_q = -1d0*(cos(kx+qx)+cos(ky+qy))
! xk = lambda*sin(kx)
! yk = lambda*sin(ky)
! xk_plus_q = lambda*sin(kx+qx)
! yk_plus_q = lambda*sin(ky+qy)
! vkq = xk*xk_plus_q + yk*yk_plus_q
! !
! Mk_t = Mh - Tz*gt + ek
! Mkq_t = Mh - Tz*gt + ek_plus_q
! !
! Ek2 = Mk_t**2 + xk**2 + yk**2
! Ekq2 = Mkq_t**2 + xk_plus_q**2 + yk_plus_q**2
! !
! do n=1,Lf
! wn = pi/beta*(2*n-1)-ImSigma(n)
! wn_plus_m = pi/beta*(2*(n+m)-1)-ImSigma(n+m)
! !
! Mk = Mh - Tz*gt + ReSigma(n) + ek
! Mk_plus_q = Mh - Tz*gt + ReSigma(n+m) + ek_plus_q
! !
! simEk = Mk**2 + xk**2 + yk**2
! simEk_plus_q = Mk_plus_q**2 + xk_plus_q**2 + yk_plus_q**2
! !
! Dk = wn**2d0 + simEk
! Dk_plus_q = wn_plus_m**2 + simEk_plus_q
! !
! num = wn*wn_plus_m - Mk*Mk_plus_q + vkq
! den = Dk*Dk_plus_q
! !
! num_t = (pi/beta*(2*n-1))*(pi/beta*(2*(n+m)-1)) - Mk_t*Mkq_t + vkq
! den_t = ((pi/beta*(2*(n+m)-1))**2d0 + Ekq2)*((pi/beta*(2*n-1))**2d0 + Ek2)
! !
! Chi = Chi + 2d0*(num/den-num_t/den_t)/beta/Nktot
! enddo
! tail_num = (Ekq2-Ek2)*(vkq-Mk_t*Mkq_t-Ek2) + (vkq-Mk_t*Mkq_t+Ek2)*nu**2d0
! tail_den = sqrt(Ek2)*((Ekq2-Ek2)**2d0 + 2d0*(Ekq2+Ek2)*nu**2d0 + nu**4d0)
! tail = tail + tanh(0.5d0*beta*sqrt(Ek2))*tail_num/tail_den/Nktot
! enddo
! Chi = Chi + tail
! end function Chi_qv
! function SumMats_Chi_kv_q(kvec) result(chi)
! real(8),dimension(:) :: kvec
! real(8) :: chi
! real(8) :: Tz,dTz
! real(8),dimension(L) :: ReSigma,ImSigma
! real(8) :: iwn,iwnm
! real(8) :: wn,wn_plus_m
! real(8) :: Mk,Mk_plus_q
! real(8) :: ek,ek_plus_q
! real(8) :: xk,xk_plus_q
! real(8) :: yk,yk_plus_q
! real(8) :: SimEk,SimEk_plus_q
! real(8) :: Dk,Dk_plus_q
! real(8) :: num,den
! real(8) :: num_t,den_t, Mk_t, Mkq_t, Ek2, Ekq2
! real(8) :: tail_num, tail_den, tail, nu
! integer :: ik,n
! real(8) :: kx,ky,qx,qy,vkq
! !
! ReSigma = p_work(1:L)
! ImSigma = p_work(L+1:2*L)
! Tz = p_work(2*L+1)
! dTz = p_work(2*L+2)
! m = m_work
! !
! kx = kvec(1)
! ky = kvec(2)
! qx = qvec_work(1)
! qy = qvec_work(2)
! nu = 2*m*pi/beta
! !
! ek = -1d0*(cos(kx)+cos(ky))
! ek_plus_q = -1d0*(cos(kx+qx)+cos(ky+qy))
! xk = lambda*sin(kx)
! yk = lambda*sin(ky)
! xk_plus_q = lambda*sin(kx+qx)
! yk_plus_q = lambda*sin(ky+qy)
! vkq = xk*xk_plus_q + yk*yk_plus_q
! !
! Mk_t = Mh - Tz*gt + ek
! Mkq_t = Mh - Tz*gt + ek_plus_q
! !
! Ek2 = Mk_t**2 + xk**2 + yk**2
! Ekq2 = Mkq_t**2 + xk_plus_q**2 + yk_plus_q**2
! !
! Chi = 0d0
! do n=1,Lf
! iwn = pi/beta*(2*n-1)
! iwnm = pi/beta*(2*(n+m)-1)
! !
! wn = iwn-ImSigma(n)
! wn_plus_m = iwnm-ImSigma(n+m)
! !
! Mk = Mh - Tz*gt + ReSigma(n) + ek
! Mk_plus_q = Mh - Tz*gt + ReSigma(n+m) + ek_plus_q
! !