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ED_Ns_AIM_final.m
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ED_Ns_AIM_final.m
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function [E,EGS,Psi,Psi_GS,NSz_GS,Problem_mat] = ED_Ns_AIM_final(ed,U,ee,V,Ns,C_ind,table,indice_sector,H_non_zero_ele,spar)
% opt.DISP = 0;
% warning off;
%opts.p = 2;
file_name_problem = 'No convergence of eigenvalues after 5 attempts for sector [N Sz] = [%d %d]';
Problem_mat = [0 0 0];
prob = 1;
if spar == 0
nb_eigen = 1;
OPTS.tol = 1e-30;%eps;
end
f = size(C_ind);
Nb_sector = f(2);
%fprintf('Number of sectors in particle number Nb_sector = %d\n\n',Nb_sector)
EGS = 0;
E = cell(f);
Psi = cell(f);
temps = tic;
for r = 1:Nb_sector
Sz_N = C_ind{1,r}(:,2);
change_spin = find(diff(Sz_N)~=0)';
indice_change_spin = change_spin+1;
split_spin_sec = [0 change_spin];
nbr_change = length(indice_change_spin);
nbr_spin_diff = nbr_change+1;
if nbr_change ~=0
hh = [change_spin(1:length(change_spin)) change_spin(length(change_spin))+1];
end
if nbr_change == 0
%tstart1 = tic;
%fprintf('\n\n Calculating sector N = %d and Sz = %d\n',r-1,Sz_N)
%fprintf('This sector has 1 state\n')
bin_num = table(C_ind{1,r}(1)+1,4);
CC = cast(dec2bin(bin_num,2*Ns),'double')-48;
CC(1,2*Ns+1) = Sz_N;
E{1,r} = Mat_element_AIM_final(CC,CC,Ns,ed,U,ee,V);
Psi{1,r} = 1;
%fprintf('The ground state of the sector is %f\n',E{1,r})
if E{1,r} < EGS
EGS = E{1,r};
Psi_GS{1,1} = Psi{1,r};
%Psi_GS = Psi{1,r};
NSz_GS = [r-1 Sz_N];
end
%toc(tstart1)
else
E{1,r} = cell(1,nbr_change);
Psi{1,r} = cell(1,nbr_change);
for h = 1:nbr_change+1;
%tstart1 = tic ;
length_spins = length(find(Sz_N == Sz_N(hh(h))));
%fprintf('\n\nCalculating sector N = %d and Sz = %d\n',r-1,Sz_N(hh(h)))
%fprintf('This sector has %d states\n',length_spins)
states_ket_ind = C_ind{1,r}(1+split_spin_sec(h):length_spins+split_spin_sec(h),:);
[lig_states,col_states] = size(states_ket_ind);
nd_states = bitget(table(states_ket_ind(:,1)+1,4),2*Ns)+bitget(table(states_ket_ind(:,1)+1,4),2*Ns-1);
D_states = bitget(table(states_ket_ind(:,1)+1,4),2*Ns).*bitget(table(states_ket_ind(:,1)+1,4),2*Ns-1);
nc_states = zeros(lig_states,Ns-1);
nc_states(lig_states,Ns-1) = 0;
for oo = 1:(Ns-1)
nc_states(:,oo) = bitget(table(states_ket_ind(:,1)+1,4),2*Ns-2*oo)+bitget(table(states_ket_ind(:,1)+1,4),2*Ns-2*oo-1);
end
diag_H = ed*nd_states + U*D_states + nc_states*ee';
L_DH = length(diag_H);
ind_diag = 1:L_DH;
clear nc_states;
if length_spins > 1
lig_col_hij = H_non_zero_ele{1,r}{1,h};
lig = lig_col_hij(2,:);
col = lig_col_hij(3,:);
hij = lig_col_hij(1,:);
lig = [lig_col_hij(2,:) ind_diag];
col = [lig_col_hij(3,:) ind_diag];
hij = sign(lig_col_hij(1,:)).*V(abs(lig_col_hij(1,:)));
hij = [hij 0.5*diag_H'];
H = sparse(lig,col,hij,L_DH,L_DH);
H = (H+H');
%full(H)
% if (spar == 0) && (length_spins > 1000)
%disp('yup')
%[eigen_val,eigen_vec] = eigifp(H,opt);
r_convergence = 0;
r_count = 1;
while r_convergence == 0;
[eigen_vec,eigen_val,Flag] = eigs(H,[],nb_eigen,'SA',OPTS);
if Flag ~= 0 && r_count ~= 5
Problem_mat(prob,1) = r-1;
Problem_mat(prob,2) = Sz_N(hh(h));
Problem_mat(prob,3) = Flag;
prob = prob + 1;
elseif Flag ~= 0 && r_count == 5
name_problem = sprintf(file_name_problem,r-1,Sz_N(hh(h)));
disp(name_problem)
Problem_mat(prob,1) = r-1;
Problem_mat(prob,2) = Sz_N(hh(h));
Problem_mat(prob,3) = Flag;
prob = prob + 1;
r_convergence = 1;
else
r_convergence = 1;
end
r_count = r_count + 1;
end
%else
% [eigen_vec,eigen_val] = eig(full(H));
%end
E{1,r}{1,h} = diag(eigen_val);
Psi{1,r}{1,h} = eigen_vec;
EGS_sec = min(E{1,r}{1,h});
%fprintf('The ground state of the sector is %f\n',EGS_sec)
if EGS_sec < EGS
[EGS,L] = min(E{1,r}{1,h});
Psi_GS{1,1} = Psi{1,r}{1,h}(:,L);
%Psi_GS = Psi{1,r}{1,h}(:,L);
NSz_GS = [r-1 Sz_N(hh(h))];
end
else
E{1,r}{1,h} = diag_H;
Psi{1,r}{1,h} = 1;
%fprintf('The ground state of the sector is %f\n',E{1,r}{1,h})
if E{1,r}{1,h} < EGS
EGS = E{1,r}{1,h};
Psi_GS{1,1} = Psi{1,r}{1,h};
%Psi_GS = Psi{1,r}{1,h};
NSz_GS = [r-1 Sz_N(hh(h))];
end
end
%toc(tstart1)
end
end
end
NSz_GSS = NSz_GS;
%EGS
%fprintf('\n\n The full diagonalization took:\n');
%toc(temps)
r_psi = 2;
disp('Starting to search for degeneracies');
if NSz_GS(2) ~= 0
new_SZ = -NSz_GS(2);
new_N_deg = NSz_GS(1);
NSz_GS = [NSz_GS;new_N_deg new_SZ]
Sz_N_max = C_ind{1,new_N_deg+1}(1,2);
dddd = length(Sz_N_max:-2:new_SZ);
Psi_GS{1,r_psi} = Psi{1, new_N_deg+1}{1,dddd};
EGS(r_psi) = E{1,new_N_deg+1}{1,dddd};
r_psi = r_psi+1;
end
%if (NSz_GSS(1) ~= Ns) && (NSz_GSS(2) ~= 0)
for dd = 1:2*Ns+1
next_loop = length(E{1,dd});
for ddd = 1:next_loop
% if dd == 1 || dd == 2*Ns+1
% diff_deg = abs(E{1,dd}-EGS);
% else
% diff_deg = abs(E{1,dd}{1,ddd}-EGS);
% end
N_electron = dd-1;
Sz_N_max = C_ind{1,dd}(1,2);
Sz_now_vec = Sz_N_max:-2:-Sz_N_max;
Sz_now = Sz_now_vec(ddd);
if ( (N_electron == NSz_GSS(1) && Sz_now ~= -NSz_GSS(2)) || (N_electron ~= NSz_GSS(1)) )
if dd == 1 || dd == 2*Ns+1
%diff_deg = abs(E{1,dd}-EGS);
a = E{1,dd};
else
%diff_deg = abs(E{1,dd}{1,ddd}-EGS);
a = E{1,dd}{1,ddd};
end
b = EGS(1);
aa = abs(a-floor(a));
bb = abs(b-floor(b));
%The tow energies are equal up to how many digits
diff_EGS = floor(abs(log10(abs(b-a))));
if diff_EGS >= 12 %(( (floor(1e12*aa)- floor(1e12*bb)) == 0 ) && ( (floor(1e13*aa)- floor(1e13*bb)) ~= 0)) || (( (floor(1e13*aa)- floor(1e13*bb)) == 0 ) && ( (floor(1e14*aa)- floor(1e14*bb)) ~= 0)) || (( (floor(1e14*aa)- floor(1e14*bb)) == 0 ) && ( (floor(1e15*aa)- floor(1e15*bb)) ~= 0)) || ( (floor(1e15*aa)- floor(1e15*bb)) == 0)
%(( (floor(1e11*aa)- floor(1e11*bb)) == 0 ) && ( (floor(1e12*aa)- floor(1e12*bb)) ~= 0)) ||
N_deg = dd-1;
Sz_N = C_ind{1,dd}(:,2);
change_spin = find(diff(Sz_N)~=0)';
indice_change_spin = change_spin+1;
split_spin_sec = [0 change_spin];
nbr_change = length(indice_change_spin);
nbr_spin_diff = nbr_change+1;
if nbr_change ~=0
hh = [change_spin(1:length(change_spin)) change_spin(length(change_spin))+1];
end
if (N_deg == NSz_GSS(1) && Sz_N(hh(ddd)) ~= NSz_GSS(2) ) || N_deg ~= NSz_GSS(1)
NSz_GS = [NSz_GS;N_deg Sz_N(hh(ddd))];
Psi_GS{1,r_psi} = Psi{1,dd}{1,ddd};
%Psi_GS(1,r_psi) = Psi{1,dd}{1,ddd};
EGS(r_psi) = a;
r_psi = r_psi+1;
end
end
end
end
end
NSz_GS
end
%end
%end