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DMRG_SUPERBLOCK_DIRECT.f90
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DMRG_SUPERBLOCK_DIRECT.f90
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MODULE DMRG_SUPERBLOCK_DIRECT
USE VARS_GLOBAL
USE DMRG_CONNECT
USE DMRG_SUPERBLOCK_COMMON
implicit none
private
public :: Setup_SuperBlock_Direct
public :: spMatVec_direct_main
contains
!##################################################################
! SETUP THE SUPERBLOCK HAMILTONIAN
! DIRECT MODE
! H^SB = H^L x 1^R + 1^L x H^R + H^LR
! H^LR = sum_p A_p x B_p
!
! * direct: get vec{A},vec{B},vec{Hleft},vec{Hright}
! the sparse matrices which reconstruct H^SB above in terms of
! conserved QN blocks:
! + H^a=L,R = [H^a[q1], H^a[q2], ... , [H^a[qN]]
! with each H^a[qi] a given block of conserved QN qi
! + A or B = [A[q1,q1'], ... , A[qN,qN']]
! with each A[q,q'] connectin the blocks of differend QN q and q'
!##################################################################
subroutine Setup_SuperBlock_Direct()
character(len=:),allocatable :: type
!
if(.not.left%operators%has_key("H"))&
stop "Setup_SuperBlock_Direct ERROR: Missing left.H operator in the list"
if(.not.right%operators%has_key("H"))&
stop "Setup_SuperBlock_Direct ERROR: Missing right.H operator in the list"
!
type=left%type()
if(type/=right%type())&
stop "Setup_SuperBlock_Direct ERROR: left.Type != right.Type"
!
!
! call start_timer("Setup SuperBlock Direct")
select case(type)
case default;stop "Setup_SuperBlock_Direct ERROR: wrong left/right.Type"
case ("spin","s")
call Setup_SuperBlock_Spin_Direct()
case ("fermion","f,","electron","e")
call Setup_SuperBlock_Fermion_Direct()
end select
! call stop_timer()
end subroutine Setup_SuperBlock_Direct
!##################################################################
! SPIN CASE
!##################################################################
subroutine Setup_SuperBlock_Spin_Direct()
integer :: Nso,Nsb
integer :: it,isb,jsb
real(8),dimension(:),allocatable :: qn,qm
type(tstates),dimension(:),allocatable :: Ai,Aj,Bi,Bj
real(8),dimension(:),allocatable :: dq
integer,dimension(:,:,:),allocatable :: tMap
type(sparse_matrix),allocatable,dimension(:) :: Sleft,Sright
real(8),dimension(:,:),allocatable :: Hij
!
if(.not.left%operators%has_key("H"))&
stop "Setup_SuperBlock_Direct ERROR: Missing left.H operator in the list"
if(.not.right%operators%has_key("H"))&
stop "Setup_SuperBlock_Direct ERROR: Missing right.H operator in the list"
!
!
!> GET THE USER DEFINED MODEL HAMILTONIAN PARAMETERS:
! Hij = Hmodel(left,right)
if(allocated(Hij))deallocate(Hij)
allocate(Hij, source=HopH)
!
!
Nso = Nspin
tNso = 3
Nsb = size(sb_sector)
!
!Massive allocation
allocate(tMap(tNso,1,1))
allocate(Dls(Nsb),Drs(Nsb),Offset(Nsb))
allocate(AI(Nsb),BI(Nsb))
allocate(AJ(Nsb),BJ(Nsb))
allocate(A(tNso,Nsb),B(tNso,Nsb))
allocate(Hleft(Nsb),Hright(Nsb))
allocate(RowOffset(tNso,Nsb),ColOffset(tNso,Nsb))
allocate(Sleft(Nspin),Sright(Nspin))
!
!Creating the sequence of operators A*_q, B*_q
! which decompose the term H^LR of the
! super-block Hamiltonian.
it = 0
do i=1,tNso
it = it+1
tMap(i,1,1)=it
enddo
!
Offset=0
do isb=1,Nsb
qn = sb_sector%qn(index=isb)
Dls(isb)= sector_qn_dim(left%sectors(1),qn)
Drs(isb)= sector_qn_dim(right%sectors(1),current_target_qn - qn)
if(isb>1)Offset(isb)=Offset(isb-1)+Dls(isb-1)*Drs(isb-1)
enddo
!
dq=[1d0]
do isb=1,size(sb_sector)
qn = sb_sector%qn(index=isb)
AI(isb)%states = sb2block_states(qn,'left')
BI(isb)%states = sb2block_states(qn,'right')
qm = qn - dq
if(.not.sb_sector%has_qn(qm))cycle
jsb = sb_sector%index(qn=qm)
AJ(jsb)%states = sb2block_states(qm,'left')
BJ(jsb)%states = sb2block_states(qm,'right')
enddo
!
do ispin=1,Nspin
Sleft(ispin) = left%operators%op("S"//left%okey(0,ispin))
Sright(ispin) = right%operators%op("S"//right%okey(0,ispin))
enddo
!
do isb=1,size(sb_sector)
qn = sb_sector%qn(index=isb)
!
!> get: H*^L and H*^R
Hleft(isb) = sp_filter(left%operators%op("H"),AI(isb)%states)
Hright(isb)= sp_filter(right%operators%op("H"),BI(isb)%states)
!> get: A = Jp*S_lz .x. B = S_rz + Row/Col Offsets
it=tMap(1,1,1)
A(it,isb) = Hij(1,1)*sp_filter(Sleft(1),AI(isb)%states,AI(isb)%states)
B(it,isb) = sp_filter(Sright(1),BI(isb)%states,BI(isb)%states)
RowOffset(it,isb)=Offset(isb)
ColOffset(it,isb)=Offset(isb)
!
dq = [1d0]
qm = qn - dq
if(.not.sb_sector%has_qn(qm))cycle
jsb = sb_sector%index(qn=qm)
!> get: A = Jxy*S_l- .x. B = [S_r-]^+=S_r+ + Row/Col Offsets
it=tMap(2,1,1)
A(it,isb) = Hij(2,2)*sp_filter(Sleft(2),AI(isb)%states,AJ(jsb)%states)
B(it,isb) = sp_filter(hconjg(Sright(2)),BI(isb)%states,BJ(jsb)%states)
RowOffset(it,isb)=Offset(isb)
ColOffset(it,isb)=Offset(jsb)!right%sectors(1)%index(qn=qm))
!> get H.c. + Row/Col Offsets
it=tMap(3,1,1)
A(it,isb) = hconjg(A(tMap(2,1,1),isb))
B(it,isb) = hconjg(B(tMap(2,1,1),isb))
RowOffset(it,isb)=Offset(jsb)!right%sectors(1)%index(qn=qm))
ColOffset(it,isb)=Offset(isb)
enddo
end subroutine Setup_SuperBlock_Spin_Direct
!##################################################################
! FERMION CASE
!##################################################################
subroutine Setup_SuperBlock_Fermion_Direct()
integer :: Nso,Nsb
integer :: it,isb,jsb
real(8),dimension(:),allocatable :: qn,qm
type(tstates),dimension(:),allocatable :: Ai,Aj,Bi,Bj
real(8),dimension(:),allocatable :: dq
real(8),dimension(2),parameter :: qnup=[1d0,0d0],qndw=[0d0,1d0]
integer,dimension(:,:,:),allocatable :: tMap
type(sparse_matrix) :: P
type(sparse_matrix),allocatable,dimension(:) :: Cleft,Cright
real(8),dimension(:,:),allocatable :: Hij
!
if(.not.left%operators%has_key("H"))&
stop "Setup_SuperBlock_Direct ERROR: Missing left.H operator in the list"
if(.not.right%operators%has_key("H"))&
stop "Setup_SuperBlock_Direct ERROR: Missing right.H operator in the list"
!
!
!> GET THE USER DEFINED MODEL HAMILTONIAN PARAMETERS:
! Hij = Hmodel(left,right)
if(allocated(Hij))deallocate(Hij)
allocate(Hij, source=HopH)
!
!
Nso = Nspin*Norb
tNso = 2*count(Hij/=0d0)
Nsb = size(sb_sector)
!
!Massive allocation
allocate(tMap(2,Nso,Nso))
allocate(Dls(Nsb),Drs(Nsb),Offset(Nsb))
allocate(AI(Nsb),BI(Nsb))
allocate(AJ(Nsb),BJ(Nsb))
allocate(A(tNso,Nsb),B(tNso,Nsb))
allocate(Hleft(Nsb),Hright(Nsb))
allocate(RowOffset(tNso,Nsb),ColOffset(tNso,Nsb))
allocate(Cleft(Nso),Cright(Nso))
!
!Creating the sequence of operators A*_q, B*_q
! which decompose the term H^LR of the
! super-block Hamiltonian.
it = 0
do i=1,2
do io=1,Nso
do jo=1,Nso
if(Hij(io,jo)==0d0)cycle
it = it+1
tMap(i,io,jo)=it
enddo
enddo
enddo
!
!
Offset=0
do isb=1,Nsb
qn = sb_sector%qn(index=isb)
Dls(isb)= sector_qn_dim(left%sectors(1),qn)
Drs(isb)= sector_qn_dim(right%sectors(1),current_target_qn - qn)
if(isb>1)Offset(isb)=Offset(isb-1)+Dls(isb-1)*Drs(isb-1)
enddo
!
do isb=1,size(sb_sector)
qn = sb_sector%qn(index=isb)
AI(isb)%states = sb2block_states(qn,'left')
BI(isb)%states = sb2block_states(qn,'right')
do ispin=1,Nspin
dq = qnup ; if(ispin==2)dq=qndw
qm = qn - dq
if(.not.sb_sector%has_qn(qm))cycle
jsb = sb_sector%index(qn=qm)
AJ(jsb)%states = sb2block_states(qm,'left')
BJ(jsb)%states = sb2block_states(qm,'right')
enddo
enddo
!
!
P = left%operators%op("P")
do ispin=1,Nspin
do iorb=1,Norb
io = iorb+(ispin-1)*Norb
Cleft(io) = left%operators%op("C"//left%okey(iorb,ispin))
Cright(io) = right%operators%op("C"//right%okey(iorb,ispin))
enddo
enddo
!
do isb=1,size(sb_sector)
qn = sb_sector%qn(index=isb)
!
!> get: H*^L and H*^R
Hleft(isb) = sp_filter(left%operators%op("H"),AI(isb)%states)
Hright(isb)= sp_filter(right%operators%op("H"),BI(isb)%states)
!
!> get A.x.B terms:
do ispin=1,Nspin
dq = qnup ; if(ispin==2)dq=qndw
qm = qn - dq
if(.not.sb_sector%has_qn(qm))cycle
jsb = sb_sector%index(qn=qm)
!
do iorb=1,Norb
do jorb=1,Norb
io = iorb+(ispin-1)*Norb
jo = jorb+(ispin-1)*Norb
if(Hij(io,jo)==0d0)cycle
!
!> get: A = H(a,b)*[Cl(a,s)^+@P] .x. B = Cr(b,s) + Row/Col Offsets
it=tMap(1,io,jo)
A(it,isb) = Hij(io,jo)*sp_filter(matmul(Cleft(io)%dgr(),P),AI(isb)%states,AJ(jsb)%states)
B(it,isb) = sp_filter(Cright(jo),BI(isb)%states,BJ(jsb)%states)
RowOffset(it,isb)=Offset(isb)
ColOffset(it,isb)=Offset(jsb)!right%sectors(1)%index(qn=qm))
!
!> get H.c. + Row/Col Offsets
it=tMap(2,io,jo)
A(it,isb) = hconjg(A(tMap(1,io,jo),isb))
B(it,isb) = hconjg(B(tMap(1,io,jo),isb))
RowOffset(it,isb)=Offset(jsb)!right%sectors(1)%index(qn=qm))
ColOffset(it,isb)=Offset(isb)
enddo
enddo
!
enddo
enddo
end subroutine Setup_SuperBlock_Fermion_Direct
!##################################################################
! SuperBlock MATRIX-VECTOR PRODUCTS
! using shared quantities in GLOBAL
!##################################################################
subroutine spMatVec_direct_main(Nloc,v,Hv)
integer :: Nloc
real(8),dimension(Nloc) :: v
real(8),dimension(Nloc) :: Hv
real(8) :: val
integer :: i,j,k,n
integer :: ir,il,jr,jl,it
integer :: arow,brow,acol,bcol,jcol
integer :: ia,ib,ic,ja,jb,jc
real(8) :: aval,bval
!
Hv=zero
!> loop over all the SB sectors:
sector: do k=1,size(sb_sector)
!
!> apply the H^L x 1^r: need to T v and Hv
do ir=1,Drs(k)
do il=1,Dls(k)
i = ir + (il-1)*Drs(k) + offset(k)
do jcol=1,Hleft(k)%row(il)%Size
val = Hleft(k)%row(il)%vals(jcol)
jl = Hleft(k)%row(il)%cols(jcol)
j = ir + (jl-1)*Drs(k) + offset(k)
Hv(i) = Hv(i) + val*v(j)
end do
enddo
enddo
!
!> apply the 1^L x H^r
do il=1,Drs(k)
do ir=1,Dls(k)
i = il + (ir-1)*Drs(k) + offset(k)
do jcol=1,Hright(k)%row(il)%Size
val = Hright(k)%row(il)%vals(jcol)
jl = Hright(k)%row(il)%cols(jcol)
j = jl + (ir-1)*Drs(k) + offset(k)
Hv(i) = Hv(i) + val*v(j)
end do
enddo
enddo
!
!> apply the term sum_k sum_it A_it(k).x.B_it(k)
do it=1,tNso
if(.not.A(it,k)%status.OR..not.B(it,k)%status)cycle
do ic=1,A(it,k)%Nrow*B(it,k)%Nrow
arow = (ic-1)/B(it,k)%Nrow+1
brow = mod(ic,B(it,k)%Nrow);if(brow==0)brow=B(it,k)%Nrow
if(A(it,k)%row(arow)%Size==0.OR.B(it,k)%row(brow)%Size==0)cycle
i = ic + RowOffset(it,k)
do ja=1,A(it,k)%row(arow)%Size
acol = A(it,k)%row(arow)%cols(ja)
aval = A(it,k)%row(arow)%vals(ja)
do jb=1,B(it,k)%row(brow)%Size
bcol = B(it,k)%row(brow)%cols(jb)
bval = B(it,k)%row(brow)%vals(jb)
! print*,j,bcol,acol,B(it,k)%Ncol,ColOffset(it,k)
! if(j>Nloc)stop "J> Nloc"
j = bcol+(acol-1)*B(it,k)%Ncol + ColOffset(it,k)
Hv(i) = Hv(i) + aval*bval*v(j)
enddo
enddo
enddo
enddo
enddo sector
end subroutine spMatVec_direct_main
END MODULE DMRG_SUPERBLOCK_DIRECT
! subroutine Setup_SuperBlock_Direct()
! integer :: Nso,Nsb
! integer :: it,isb,jsb
! real(8),dimension(:),allocatable :: qn,qm
! type(tstates),dimension(:),allocatable :: Ai,Aj,Bi,Bj
! real(8),dimension(:),allocatable :: dq
! real(8),dimension(2),parameter :: qnup=[1d0,0d0],qndw=[0d0,1d0]
! integer,dimension(:,:,:),allocatable :: tMap
! type(sparse_matrix) :: P
! type(sparse_matrix),allocatable,dimension(:) :: Cleft,Cright
! type(sparse_matrix),allocatable,dimension(:) :: Sleft,Sright
! real(8),dimension(:,:),allocatable :: Hij
! integer :: m_left,m_right
! character(len=:),allocatable :: type
! !
! if(.not.left%operators%has_key("H"))&
! stop "Setup_SuperBlock_Direct ERROR: Missing left.H operator in the list"
! if(.not.right%operators%has_key("H"))&
! stop "Setup_SuperBlock_Direct ERROR: Missing right.H operator in the list"
! !
! type=left%type()
! if(type/=right%type())&
! stop "Setup_SuperBlock_Direct ERROR: left.Type != right.Type"
! !
! m_left = left%dim
! m_right= right%dim
! !
! !> GET THE USER DEFINED MODEL HAMILTONIAN PARAMETERS:
! Hij = Hmodel(left,right)
! !
! !
! select case(type)
! case default;stop "Setup_SuperBlock_Direct ERROR: wrong left/right.Type"
! case ("spin","s")
! Nso = Nspin
! case ("fermion","f,","electron","e")
! Nso = Nspin*Norb
! end select
! !
! Nsb = size(sb_sector)
! !
! !Creating the sequence of operators A*_q, B*_q
! ! which decompose the term H^LR of the
! ! super-block Hamiltonian.
! select case(type)
! case default;stop "Setup_SuperBlock_Direct ERROR: wrong left/right.Type"
! case ("spin","s")
! tNso = 3
! allocate(tMap(3,1,1))
! it = 0
! do i=1,tNso
! it = it+1
! tMap(i,1,1)=it
! enddo
! case ("fermion","f,","electron","e")
! tNso = 2*count(Hij/=0d0)
! allocate(tMap(2,Nso,Nso))
! it = 0
! do i=1,2
! do io=1,Nso
! do jo=1,Nso
! if(Hij(io,jo)==0d0)cycle
! it = it+1
! tMap(i,io,jo)=it
! enddo
! enddo
! enddo
! end select
! !
! allocate(Dls(Nsb),Drs(Nsb),Offset(Nsb))
! Offset=0
! do isb=1,Nsb
! qn = sb_sector%qn(index=isb)
! Dls(isb)= sector_qn_dim(left%sectors(1),qn)
! Drs(isb)= sector_qn_dim(right%sectors(1),current_target_qn - qn)
! if(isb>1)Offset(isb)=Offset(isb-1)+Dls(isb-1)*Drs(isb-1)
! enddo
! !
! print*,"DIMS:",sum(Dls),sum(Drs)
! allocate(AI(Nsb),BI(Nsb))
! allocate(AJ(Nsb),BJ(Nsb))
! select case(type)
! case default;stop "Setup_SuperBlock_Direct ERROR: wrong left/right.Type"
! case ("spin","s")
! dq=[1d0]
! do isb=1,size(sb_sector)
! qn = sb_sector%qn(index=isb)
! AI(isb)%states = sb2block_states(qn,'left')
! BI(isb)%states = sb2block_states(qn,'right')
! print*,size(BI(isb)%states),Drs(isb),Dls(isb)
! qm = qn - dq
! if(.not.sb_sector%has_qn(qm))cycle
! jsb = sb_sector%index(qn=qm)
! AJ(jsb)%states = sb2block_states(qm,'left')
! BJ(jsb)%states = sb2block_states(qm,'right')
! enddo
! case ("fermion","f,","electron","e")
! do isb=1,size(sb_sector)
! qn = sb_sector%qn(index=isb)
! AI(isb)%states = sb2block_states(qn,'left')
! BI(isb)%states = sb2block_states(qn,'right')
! do ispin=1,Nspin
! dq = qnup ; if(ispin==2)dq=qndw
! qm = qn - dq
! if(.not.sb_sector%has_qn(qm))cycle
! jsb = sb_sector%index(qn=qm)
! AJ(jsb)%states = sb2block_states(qm,'left')
! BJ(jsb)%states = sb2block_states(qm,'right')
! enddo
! enddo
! end select
! !
! !
! allocate(A(tNso,Nsb),B(tNso,Nsb))
! allocate(Hleft(Nsb),Hright(Nsb))
! allocate(RowOffset(tNso,Nsb),ColOffset(tNso,Nsb))
! select case(type)
! case default;stop "Setup_SuperBlock_Direct ERROR: wrong left/right.Type"
! case ("spin","s")
! allocate(Sleft(Nspin),Sright(Nspin))
! do ispin=1,Nspin
! Sleft(ispin) = left%operators%op("S"//left%okey(0,ispin))
! Sright(ispin) = right%operators%op("S"//right%okey(0,ispin))
! enddo
! !
! print*,"Constructing H^{L,R}*: the filtered block Hamiltonians"
! do isb=1,size(sb_sector)
! qn = sb_sector%qn(index=isb)
! !
! !> get: H*^L and H*^R
! Hleft(isb) = sp_filter(left%operators%op("H"),AI(isb)%states)
! Hright(isb)= sp_filter(right%operators%op("H"),BI(isb)%states)
! print*,"L",shape(Hleft(isb)),Dls(isb)
! print*,"R",shape(Hright(isb)),Drs(isb)
! !> get: A = Jp*S_lz .x. B = S_rz + Row/Col Offsets
! it=tMap(1,1,1)
! A(it,isb) = Hij(1,1)*sp_filter(Sleft(1),AI(isb)%states,AI(isb)%states)
! B(it,isb) = sp_filter(Sright(1),BI(isb)%states,BI(isb)%states)
! RowOffset(it,isb)=Offset(isb)
! ColOffset(it,isb)=Offset(isb)
! !
! dq = [1d0]
! qm = qn - dq
! if(.not.sb_sector%has_qn(qm))cycle
! jsb = sb_sector%index(qn=qm)
! !> get: A = Jp*S_l- .x. B = [S_r-]^+=S_r+ + Row/Col Offsets
! it=tMap(2,1,1)
! A(it,isb) = Hij(2,2)*sp_filter(Sleft(2),AI(isb)%states,AJ(jsb)%states)
! B(it,isb) = sp_filter(hconjg(Sright(2)),BI(isb)%states,BJ(jsb)%states)
! RowOffset(it,isb)=Offset(isb)
! ColOffset(it,isb)=Offset(jsb)!right%sectors(1)%index(qn=qm))
! !> get H.c. + Row/Col Offsets
! it=tMap(3,1,1)
! A(it,isb) = hconjg(A(tMap(2,1,1),isb))
! B(it,isb) = hconjg(B(tMap(2,1,1),isb))
! RowOffset(it,isb)=Offset(jsb)!right%sectors(1)%index(qn=qm))
! ColOffset(it,isb)=Offset(isb)
! enddo
! case ("fermion","f,","electron","e")
! allocate(Cleft(Nso),Cright(Nso))
! P = left%operators%op("P")
! do ispin=1,Nspin
! do iorb=1,Norb
! io = iorb+(ispin-1)*Norb
! Cleft(io) = left%operators%op("C"//left%okey(iorb,ispin))
! Cright(io) = right%operators%op("C"//right%okey(iorb,ispin))
! enddo
! enddo
! print*,"Constructing H^{L,R}*: the filtered block Hamiltonians"
! do isb=1,size(sb_sector)
! qn = sb_sector%qn(index=isb)
! !
! !> get: H*^L and H*^R
! Hleft(isb) = sp_filter(left%operators%op("H"),AI(isb)%states)
! Hright(isb)= sp_filter(right%operators%op("H"),BI(isb)%states)
! !
! !> get A.x.B terms:
! do ispin=1,Nspin
! dq = qnup ; if(ispin==2)dq=qndw
! qm = qn - dq
! if(.not.sb_sector%has_qn(qm))cycle
! jsb = sb_sector%index(qn=qm)
! !
! do iorb=1,Norb
! do jorb=1,Norb
! io = iorb+(ispin-1)*Norb
! jo = jorb+(ispin-1)*Norb
! if(Hij(io,jo)==0d0)cycle
! !
! !> get: A = H(a,b)*[Cl(a,s)^+@P] .x. B = Cr(b,s) + Row/Col Offsets
! it=tMap(1,io,jo)
! A(it,isb) = Hij(io,jo)*sp_filter(matmul(Cleft(io)%dgr(),P),AI(isb)%states,AJ(jsb)%states)
! B(it,isb) = sp_filter(Cright(jo),BI(isb)%states,BJ(jsb)%states)
! RowOffset(it,isb)=Offset(isb)
! ColOffset(it,isb)=Offset(right%sectors(1)%index(qn=qm))
! !
! !> get H.c. + Row/Col Offsets
! it=tMap(2,io,jo)
! A(it,isb) = hconjg(A(tMap(1,io,jo),isb))
! B(it,isb) = hconjg(B(tMap(1,io,jo),isb))
! RowOffset(it,isb)=Offset(right%sectors(1)%index(qn=qm))
! ColOffset(it,isb)=Offset(isb)
! enddo
! enddo
! !
! enddo
! enddo
! end select
! !
! print*,"Done:"
! print*,"######################################"
! print*,""
! end subroutine Setup_SuperBlock_Direct