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assembleHamiltonian.m
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assembleHamiltonian.m
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%<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
function [H_alpha,H_beta] = assembleHamiltonian(state_multiplicity,...
tensors,SpinOp,Qtensors,SpinXiXjOp,...
theory,isMethyl,methylMethod, methylTunnelingSplitting, methylID)
useEZ = theory(1);
useNZ = theory(2);
useHF_SzIz = theory(3);
useHF_SzIxy = theory(4);
useNucA = theory(5);
useNucB = theory(6);
useNucCD = theory(7);
useNucEF = theory(8);
useNQ = theory(9);
% Methyl version 2
useMethyl = methylMethod>0;
clusterSize = numel(state_multiplicity);
Hnuc = 0;
Hhf = 0;
% iSpin is the index of the nuclear spin in the cluster
for iSpin = 1:clusterSize
% the ith nuclear spin in the input Hamiltonian
% inucleus = ispin - zeroIndex + 1; % since the electron is given position 1
%------------------------------------------------------------------------
% One Nucleus Spin Hamiltonian
%------------------------------------------------------------------------
% Calculate nuclear Zeeman Hamiltonian
[ze,pe,me] = spinopidx(clusterSize,iSpin);
Iz = SpinOp(:,:,ze);
Ix = (SpinOp(:,:,pe) + SpinOp(:,:,me) )/2;
Iy = (SpinOp(:,:,pe) - SpinOp(:,:,me) )/2i;
if useNZ
H_nuclear_Zeeman = tensors(2,2,iSpin+1,iSpin+1)*Iy;
H_nuclear_Zeeman = H_nuclear_Zeeman + tensors(3,3,iSpin+1,iSpin+1)*Iz ...
+ tensors(1,1,iSpin+1,iSpin+1)*Ix;
else
H_nuclear_Zeeman = 0;
end
% Calculate hyperfine Hamiltonian
A = tensors(:,:,1,iSpin+1) + tensors(:,:,iSpin+1,1);
if useHF_SzIz
H_hyperfine_SzIz = A(3,3)*Iz;
else
H_hyperfine_SzIz = 0;
end
if useHF_SzIxy
H_hyperfine_SzIx = A(3,1)*Ix;
H_hyperfine_SzIy = A(3,2)*Iy;
else
H_hyperfine_SzIx = 0;
H_hyperfine_SzIy = 0;
end
% Calculate nuclear quadrupole Hamiltonian
if useNQ && state_multiplicity(iSpin) > 2
Q_ = Qtensors(:,:,iSpin);
[xx,xy,xz,yx,yy,yz,zx,zy,zz] = spinopidx_nq(iSpin,SpinXiXjOp);
H_nuclear_quadrupole = ...
Q_(1,1)*SpinXiXjOp(:,:,xx) + ...
Q_(1,2)*SpinXiXjOp(:,:,xy) + ...
Q_(1,3)*SpinXiXjOp(:,:,xz) + ...
Q_(2,1)*SpinXiXjOp(:,:,yx) + ...
Q_(2,2)*SpinXiXjOp(:,:,yy) + ...
Q_(2,3)*SpinXiXjOp(:,:,yz) + ...
Q_(3,1)*SpinXiXjOp(:,:,zx) + ...
Q_(3,2)*SpinXiXjOp(:,:,zy) + ...
Q_(3,3)*SpinXiXjOp(:,:,zz);
else
H_nuclear_quadrupole = 0;
end
% Assemble single-nucleus terms in nuclear Hamiltonian
Hnuc = Hnuc + H_nuclear_Zeeman + H_nuclear_quadrupole;
Hhf = Hhf + H_hyperfine_SzIz + H_hyperfine_SzIx + H_hyperfine_SzIy;
%------------------------------------------------------------------------
% Loop over all nuclei with index greater than the ith nucleus.
%------------------------------------------------------------------------
for jSpin = iSpin+1:clusterSize
% the jth nuclear spin in the input Hamiltonian
%jnucleus = jspin - zeroIndex + 1; % since the electron is given position 1
% get dipolar coupling tensor
dd = tensors(:,:,iSpin+1,jSpin+1) + tensors(:,:,jSpin+1,iSpin+1);
[zz,rl,lr,zr,zl,rz,lz,rr,ll] = spinopidx2(clusterSize,iSpin,jSpin);
if useNucA
IzJz = SpinOp(:,:,zz);
Hnn_A = dd(3,3)*IzJz;
else
Hnn_A = 0;
end
% nucleus-nucleus pseudo-secular (B term)
if useNucB
IpJm = SpinOp(:,:,rl);
ImJp = SpinOp(:,:,lr);
Hnn_B = 0.25*(dd(1,1) + dd(2,2))*(IpJm+ImJp);
else
Hnn_B = 0;
end
% nucleus-nucleus dipolar C and D terms
if useNucCD
IzJp = SpinOp(:,:,zr);
IpJz = SpinOp(:,:,rz);
IzJm = SpinOp(:,:,zl);
ImJz = SpinOp(:,:,lz);
cd = 1/2*(dd(1,3) - 1i*dd(2,3));
Hnn_CD = cd*(IzJp+IpJz) + cd'*(IzJm+ImJz);
else
Hnn_CD = 0;
end
% nucleus-nucleus dipolar E and F terms
if useNucEF
IpJp = SpinOp(:,:,rr);
ImJm = SpinOp(:,:,ll);
ef = 1/4*(dd(1,1) - dd(2,2) - 1i*(dd(1,2) + dd(2,1)));
Hnn_EF = ef*IpJp + ef'*ImJm;
else
Hnn_EF = 0;
end
if useMethyl && isMethyl(iSpin) && isMethyl(jSpin) ...
&& methylID(iSpin) == methylID(jSpin) %&& sum(methylID==methylID(iSpin))==3
IzJz = SpinOp(:,:,zz);
IpJm = SpinOp(:,:,rl);
ImJp = SpinOp(:,:,lr);
Jmethyl = -2/3*full( methylTunnelingSplitting(iSpin,jSpin) );
H_methyl = 0;
%H_methyl = Jmethyl*(IzJz + 0.5*IpJm + 0.5*ImJp);
if useNucA
H_methyl = H_methyl + Jmethyl*IzJz;
end
if useNucB
H_methyl = H_methyl + Jmethyl*(0.5*IpJm + 0.5*ImJp);
end
else
H_methyl = 0;
end
Hnuc = Hnuc + Hnn_A + Hnn_B + Hnn_CD + Hnn_EF + H_methyl;
end
end
% Calculate electron Zeeman Hamiltonian
if useEZ
eZeeman = tensors(:,:,1,1); % Hz
HEZ = eZeeman(3,3)*eye(size(Hnuc)); % Hz
else
HEZ = 0;
end
% Calculate total nuclear Hamiltonians for alpha and beta electron manifolds
H_alpha = +1/2*(HEZ + Hhf) + Hnuc;
H_beta = -1/2*(HEZ + Hhf) + Hnuc;
% Check Hermitianity
threshold = 1e-12;
[isHermA,nonHermiticityA] = isHermitian(H_alpha,threshold);
[isHermB,nonHermiticityB] = isHermitian(H_beta,threshold);
if ~isHermA || ~isHermB
hline = '--------------------------------------------------------------';
disp('!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!');
fprintf('Non-Hermiticity = {%d,%d}.\n',nonHermiticityA,nonHermiticityB);
disp(hline);
[isHerm,nonHermiticity] = isHermitian(HEZ,threshold);
fprintf('HEZ non-Hermiticity = %d.\n',nonHermiticity);
fprintf('pass = %d.\n',isHerm); disp(hline);
[isHerm,nonHermiticity] = isHermitian(Hhf,threshold);
fprintf('Hhf non-Hermiticity = %d.\n',nonHermiticity);
fprintf('pass = %d.\n',isHerm); disp(hline);
[isHerm,nonHermiticity] = isHermitian(H_hyperfine_SzIz,threshold);
fprintf(' H_hyperfine_SzIz non-Hermiticity = %d.\n',nonHermiticity);
fprintf(' pass = %d.\n',isHerm); disp(hline);
[isHerm,nonHermiticity] = isHermitian(H_hyperfine_SzIy,threshold);
fprintf(' H_hyperfine_SzIy non-Hermiticity = %d.\n',nonHermiticity);
fprintf(' pass = %d.\n',isHerm); disp(hline);
[isHerm,nonHermiticity] = isHermitian(H_hyperfine_SzIx,threshold);
fprintf(' H_hyperfine_SzIx non-Hermiticity = %d.\n',nonHermiticity);
fprintf(' pass = %d.\n',isHerm); disp(hline);
[isHerm,nonHermiticity] = isHermitian(Hnuc,threshold);
fprintf('Hnuc non-Hermiticity = %d.\n',nonHermiticity);
fprintf('pass = %d.\n',isHerm); disp(hline);
if clusterSize > 1
[isHerm,nonHermiticity] = isHermitian(Hnn_A,threshold);
fprintf(' Hnn_A non-Hermiticity = %d.\n',nonHermiticity);
fprintf(' pass = %d.\n',isHerm); disp(hline);
[isHerm,nonHermiticity] = isHermitian(Hnn_B,threshold);
fprintf(' Hnn_B non-Hermiticity = %d.\n',nonHermiticity);
fprintf(' pass = %d.\n',isHerm); disp(hline);
[isHerm,nonHermiticity] = isHermitian(Hnn_CD,threshold);
fprintf(' Hnn_CD non-Hermiticity = %d.\n',nonHermiticity);
fprintf(' pass = %d.\n',isHerm); disp(hline);
[isHerm,nonHermiticity] = isHermitian(Hnn_EF,threshold);
fprintf(' Hnn_EF non-Hermiticity = %d.\n',nonHermiticity);
fprintf(' pass = %d.\n',isHerm); disp(hline);
[isHerm,nonHermiticity] = isHermitian(H_nuclear_quadrupole,threshold);
fprintf(' H_nuclear_quadrupole non-Hermiticity = %d.\n',nonHermiticity);
fprintf(' pass = %d.\n',isHerm); disp(hline);
[isHerm,nonHermiticity] = isHermitian(H_methyl,threshold);
fprintf(' H_methyl non-Hermiticity = %d.\n',nonHermiticity);
fprintf(' pass = %d.\n',isHerm); disp(hline);
end
disp('!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!');
test_spinopidx();
test_spinopidx2()
test_spinops(SpinOp,clusterSize);
error('Cluster Hamiltonian is not Hermitian.');
end
% Hermitianize
H_alpha = (H_alpha+H_alpha')/2;
H_beta = (H_beta+H_beta')/2;
end
%{
--------------------------------------------------------------------------
ENUM 1-Clusters: E O
--------------------------------------------------------------------------
E (1) : E
O (2-4): z + -
--------------------------------------------------------------------------
2-Clusters: EE EO OE OO
--------------------------------------------------------------------------
EE (1) : EE
EO (2-4) : Ez E+ E-
OE (5-7) : zE +E -E
OO (8-10): zz +- -+
--------------------------------------------------------------------------
ENUM 3-Clusters: EEE EEO EOE OEE EOO OEO OOE
--------------------------------------------------------------------------
EEE (1) : EEE
EEO (2-4) : EEz EE+ EE-
EOE (5-7) : EzE E+E E-E
OEE (8-10) : zEE +EE -EE
EOO (11-13): Ezz E+- E-+
OEO (14-16): zEz +E- -E+
OOE (17-19): zzE +-E -+E
--------------------------------------------------------------------------
ENUM 4-Clusters: EEEE EEEO EEOE EOEE OEEE EEOO EOEO OEEO EOOE OEOE OOEE
--------------------------------------------------------------------------
EEEE (1) : EEEE
EEEO (2-4) : EEEz EEE+ EEE-
EEOE (5-7) : EEzE EE+E EE-E
EOEE (8-10) : EzEE E+EE E-EE
OEEE (11-13): zEEE +EEE -EEE
EEOO (14-16): EEzz EE+- EE-+
EOEO (17-19): EzEz E+E- -E+E
OEEO (20-22): zEEz +EE- -EE+
EOOE (23-25): EzzE E+-E E-+E
OEOE (26-28): zEzE +E-E -E+E
OOEE (29-31): zzEE +-EE -+EE
--------------------------------------------------------------------------
ENUM 5-Clusters
--------------------------------------------------------------------------
EEEEE (1) : EEEEE
EEEEO (2-4) : EEEEz EEEE+ EEEE-
EEEOE (5-7) : EEEzE EEE+E EEE-E
EEOEE (8-10) : EEzEE EE+EE EE-EE
EOEEE (11-13): EzEEE E+EEE E-EEE
OEEEE (14-16): zEEEE +EEEE -EEEE
EEEOO (17-19): EEEzz EEE+- EEE-+
EEOEO (20-22): EEzEz EE+E- EE-E+
EOEEO (23-25): EzEEz E+EE- E-EE+
OEEEO (26-28): zEEEz +EEE- -EEE+
EEOOE (29-31): EEzzE EE+-E EE-+E
EOEOE (32-34): EzEzE E+E-E E-E+E
EOEOE (35-37): zEEzE +EE-E -EE+E
EOOEE (38-40): EzzEE E+-EE E-+EE
OEOEE (41-43): zEzEE +E-EE -E+EE
OOEEE (44-46): zzEEE +-EEE -+EEE
--------------------------------------------------------------------------
ENUM 6-Clusters
--------------------------------------------------------------------------
EEEEEE (1) : EEEEEE
EEEEEO (2-4) : EEEEEz EEEEE+ EEEEE-
EEEEOE (5-7) : EEEEzE EEEE+E EEEE-E
EEEOEE (8-10) : EEEzEE EEE+EE EEE-EE
EEOEEE (11-13): EEzEEE EE+EEE EE-EEE
EOEEEE (14-16): EzEEEE +EEEEE -EEEEE
OEEEEE (17-19): zEEEEE +EEEEE -EEEEE
EEEEOO (20-22): EEEEzz EEEE+- EEEE-+
EEEOEO (23-25): EEEzEz EEE+E- EEE-E+
EEOEEO (26-28): EEzEEz EE+EE- EE-EE+
EOEEEO (29-31): EzEEEz E+EEE- E-EEE+
OEEEEO (32-34): zEEEEz +EEEE- -EEEE+
EEEOOE (35-37): EEEzzE EEE+-E EEE-+E
EEOEOE (38-40): EEzEzE EE+E-E EE-E+E
EOEEOE (41-43): EzEEzE E+EE-E E-EE+E
OEEEOE (44-46): zEEEzE +EEE-E -EEE+E
EEOOEE (47-49): EEzzEE EE+-EE EE-+EE
EOEOEE (50-51): EzEzEE E+E-EE E-E+EE
OEEOEE (53-55): zEEzEE +EE-EE -EE+EE
EOOEEE (56-58): EzzEEE E+-EEE E-+EEE
OEOEEE (59-61): zEzEEE +E-EEE -E+EEE
OOEEEE (62-64): zzEEEE +-EEEE -+EEEE
%}
function [z,r,l] = spinopidx(clusterSize,iSpin)
zrl = [2,3,4] + 3*(clusterSize - iSpin);
z = zrl(1);
r = zrl(2);
l = zrl(3);
end
function [z,r,l] = spinopidx_v0(clusterSize,iSpin)
switch clusterSize
case 1
% E = 1;
Z = 2; R = 3; L = 4;
zrl = [Z R L];
case 2
% EE = 1;
EZ = 2; ER = 3; EL = 4;
ZE = 5; RE = 6; LE = 7;
switch iSpin
case 1, zrl = [ZE RE LE];
case 2, zrl = [EZ ER EL];
end
case 3
% EEE = 1;
EEZ = 2; EER = 3; EEL = 4;
EZE = 5; ERE = 6; ELE = 7;
ZEE = 8; REE = 9; LEE = 10;
switch iSpin
case 3, zrl = [EEZ EER EEL];
case 2, zrl = [EZE ERE ELE];
case 1, zrl = [ZEE REE LEE];
end
case 4
% EEEE = 1;
EEEZ = 2; EEER = 3; EEEL = 4;
EEZE = 5; EERE = 6; EELE = 7;
EZEE = 8; EREE = 9; ELEE = 10;
ZEEE = 11; REEE = 12; LEEE = 13;
switch iSpin
case 4, zrl = [EEEZ EEER EEEL];
case 3, zrl = [EEZE EERE EELE];
case 2, zrl = [EZEE EREE ELEE];
case 1, zrl = [ZEEE REEE LEEE];
end
case 5
% EEEEE = 1;
EEEEZ = 2; EEEER = 3; EEEEL = 4;
EEEZE = 5; EEERE = 6; EEELE = 7;
EEZEE = 8; EEREE = 9; EELEE = 10;
EZEEE = 11; EREEE = 12; ELEEE = 13;
ZEEEE = 14; REEEE = 15; LEEEE = 16;
switch iSpin
case 5, zrl = [EEEEZ EEEER EEEEL];
case 4, zrl = [EEEZE EEERE EEELE];
case 3, zrl = [EEZEE EEREE EELEE];
case 2, zrl = [EZEEE EREEE ELEEE];
case 1, zrl = [ZEEEE REEEE LEEEE];
end
case 6
% EEEEEE = 1;
EEEEEZ = 2; EEEEER = 3; EEEEEL = 4;
EEEEZE = 5; EEEERE = 6; EEEELE = 7;
EEEZEE = 8; EEEREE = 9; EEELEE = 10;
EEZEEE = 11; EEREEE = 12; EELEEE = 13;
EZEEEE = 14; EREEEE = 15; ELEEEE = 16;
ZEEEEE = 17; REEEEE = 18; LEEEEE = 19;
switch iSpin
case 6, zrl = [EEEEEZ EEEEER EEEEEL];
case 5, zrl = [EEEEZE EEEERE EEEELE];
case 4, zrl = [EEEZEE EEEREE EEELEE];
case 3, zrl = [EEZEEE EEREEE EELEEE];
case 2, zrl = [EZEEEE EREEEE ELEEEE];
case 1, zrl = [ZEEEEE REEEEE LEEEEE];
end
end
z = zrl(1);
r = zrl(2);
l = zrl(3);
end
function test_spinopidx()
for clusterSize = 1:6
for iSpin = 1:clusterSize
[z0,r0,l0] = spinopidx_v0(clusterSize,iSpin);
zrl0 = [z0,r0,l0];
[z,r,l] = spinopidx(clusterSize,iSpin);
zrl1 = [z,r,l];
if(max( abs(zrl1-zrl0))>0)
fprintf(['\n\nError in spinopidx(): ', ...
'for cluster size %d, single spin indices are \n'],clusterSize);
disp(zrl1);
disp('when they should be');
disp(zrl0);
error('Error above.');
end
end
end
end
function [zz,rl,lr,zr,zl,rz,lz,rr,ll] = spinopidx2(clusterSize,iSpin,jSpin)
iParticle = clusterSize + 1 -iSpin;
jParticle = clusterSize + 1 -jSpin;
% ZZ RL LR ------------------
offset = 3*clusterSize -1;
m = iParticle-jParticle;
n = jParticle-1;
zzIncrementation = m + clusterSize*n -(n^2 + n)/2;
zz = 3*zzIncrementation + offset;
rl = zz + 1;
lr = rl + 1;
% ZR ZL RZ LZ------------------
m = clusterSize - (clusterSize - 1);
n = clusterSize - 2;
zzOffset = m + clusterSize*n -(n^2 + n)/2;
offset = offset + 3*zzOffset + 3;
zr = 4*( zzIncrementation -1) + offset;
zl = zr + 1;
rz = zl + 1;
lz = rz + 1;
% RR LL ------------------
offset = offset + 4*zzOffset;
rr = 2*( zzIncrementation -1) + offset;
ll = rr + 1;
end
function [zz,rl,lr,zr,zl,rz,lz,rr,ll] = spinopidx2_v0(clusterSize,iSpin,jSpin)
switch clusterSize
case 2
ZZ = 8; RL = 9; LR = 10;
ZR = 11; ZL = 12; RZ = 13;
LZ = 14; RR = 15; LL = 16;
IJ = [ZZ RL LR ZR ZL RZ LZ RR LL];
case 3
% ZZ RL LR ------------------
EZZ = 11; ERL = 12; ELR = 13;
ZEZ = 14; REL = 15; LER = 16;
ZZE = 17; RLE = 18; LRE = 19;
% ZR ZL RZ LZ------------------
EZR = 20; EZL = 21; ERZ = 22; ELZ = 23;
ZER = 24; ZEL = 25; REZ = 26; LEZ = 27;
ZRE = 28; ZLE = 29; RZE = 30; LZE = 31;
% RR LL ------------------
ERR = 32; ELL = 33;
RER = 34; LEL = 35;
RRE = 36; LLE = 37;
switch iSpin
case 1 % OOE or OEO
switch jSpin
case 3, IJ = [ZEZ REL LER ZER ZEL REZ LEZ RER LEL]; % OEO
case 2, IJ = [ZZE RLE LRE ZRE ZLE RZE LZE RRE LLE]; % OOE
end
case 2, IJ = [EZZ ERL ELR EZR EZL ERZ ELZ ERR ELL]; % EOO
end
case 4
% ZZ RL LR ------------------
EEZZ = 14; EERL = 15; EELR = 16;
EZEZ = 17; EREL = 18; ELER = 19;
ZEEZ = 20; REEL = 21; LEER = 22;
EZZE = 23; ERLE = 24; ELRE = 25;
ZEZE = 26; RELE = 27; LERE = 28;
ZZEE = 29; RLEE = 30; LREE = 31;
% ZR ZL RZ LZ------------------
EEZR = 32; EEZL = 33; EERZ = 34; EELZ = 35;
EZER = 36; EZEL = 37; EREZ = 38; ELEZ = 39;
ZEER = 40; ZEEL = 41; REEZ = 42; LEEZ = 43;
EZRE = 44; EZLE = 45; ERZE = 46; ELZE = 47;
ZERE = 48; ZELE = 49; REZE = 50; LEZE = 51;
ZREE = 52; ZLEE = 53; RZEE = 54; LZEE = 55;
% RR LL ------------------
EERR = 56; EELL = 57;
ERER = 58; ELEL = 59;
REER = 60; LEEL = 61;
ERRE = 62; ELLE = 63;
RERE = 64; LELE = 65;
RREE = 66; LLEE = 67;
switch iSpin
case 1
switch jSpin
case 4, IJ = [ZEEZ REEL LEER ZEER ZEEL REEZ LEEZ REER LEEL]; % OEEO
case 3, IJ = [ZEZE RELE LERE ZERE ZELE REZE LEZE RERE LELE]; % OEOE
case 2, IJ = [ZZEE RLEE LREE ZREE ZLEE RZEE LZEE RREE LLEE]; % OOEE
end
case 2
switch jSpin
case 4, IJ = [EZEZ EREL ELER EZER EZEL EREZ ELEZ ERER ELEL]; % EOEO
case 3, IJ = [EZZE ERLE ELRE EZRE EZLE ERZE ELZE ERRE ELLE]; % EOOE
end
case 3, IJ = [EEZZ EERL EELR EEZR EEZL EERZ EELZ EERR EELL]; % EEOO
end
case 5
EEEZZ = 17; EEERL = 18; EEELR = 19;
EEZEZ = 20; EEREL = 21; EELER = 22;
EZEEZ = 23; EREEL = 24; ELEER = 25;
ZEEEZ = 26; REEEL = 27; LEEER = 28;
EEZZE = 29; EERLE = 30; EELRE = 31;
EZEZE = 32; ERELE = 33; ELERE = 34;
ZEEZE = 35; REELE = 36; LEERE = 37;
EZZEE = 38; ERLEE = 39; ELREE = 40;
ZEZEE = 41; RELEE = 42; LEREE = 43;
ZZEEE = 44; RLEEE = 45; LREEE = 46;
EEEZR = 47; EEEZL = 48; EEERZ = 49;
EEELZ = 50; EEZER = 51; EEZEL = 52;
EEREZ = 53; EELEZ = 54; EZEER = 55;
EZEEL = 56; EREEZ = 57; ELEEZ = 58;
ZEEER = 59; ZEEEL = 60; REEEZ = 61;
LEEEZ = 62; EEZRE = 63; EEZLE = 64;
EERZE = 65; EELZE = 66; EZERE = 67;
EZELE = 68; EREZE = 69; ELEZE = 70;
ZEERE = 71; ZEELE = 72; REEZE = 73;
LEEZE = 74; EZREE = 75; EZLEE = 76;
ERZEE = 77; ELZEE = 78; ZEREE = 79;
ZELEE = 80; REZEE = 81; LEZEE = 82;
ZREEE = 83; ZLEEE = 84; RZEEE = 85;
LZEEE = 86; EEERR = 87; EEELL = 88;
EERER = 89; EELEL = 90; EREER = 91;
ELEEL = 92; REEER = 93; LEEEL = 94;
EERRE = 95; EELLE = 96; ERERE = 97;
ELELE = 98; REERE = 99; LEELE = 100;
ERREE = 101; ELLEE = 102; REREE = 103;
LELEE = 104; RREEE = 105; LLEEE = 106;
switch iSpin
case 1
switch jSpin
case 5, IJ = [ZEEEZ REEEL LEEER ZEEER ZEEEL REEEZ LEEEZ REEER LEEEL]; % OEEEO
case 4, IJ = [ZEEZE REELE LEERE ZEERE ZEELE REEZE LEEZE REERE LEELE]; % OEEOE
case 3, IJ = [ZEZEE RELEE LEREE ZEREE ZELEE REZEE LEZEE REREE LELEE]; % OEOEE
case 2, IJ = [ZZEEE RLEEE LREEE ZREEE ZLEEE RZEEE LZEEE RREEE LLEEE]; % OOEEE
end
case 2
switch jSpin
case 5, IJ = [EZEEZ EREEL ELEER EZEER EZEEL EREEZ ELEEZ EREER ELEEL]; % EOEEO
case 4, IJ = [EZEZE ERELE ELERE EZERE EZELE EREZE ELEZE ERERE ELELE]; % EOEOE
case 3, IJ = [EZZEE ERLEE ELREE EZREE EZLEE ERZEE ELZEE ERREE ELLEE]; % EOOEE
end
case 3
switch jSpin
case 5, IJ = [EEZEZ EEREL EELER EEZER EEZEL EEREZ EELEZ EERER EELEL]; % EEOEO
case 4, IJ = [EEZZE EERLE EELRE EEZRE EEZLE EERZE EELZE EERRE EELLE]; % EEOOE
end
case 4, IJ = [EEEZZ EEERL EEELR EEEZR EEEZL EEERZ EEELZ EEERR EEELL]; % EEEOO
end
case 6
% ZZ RL LR ------------------
EEEEZZ = 20; EEEERL = 21; EEEELR = 22;
EEEZEZ = 23; EEEREL = 24; EEELER = 25;
EEZEEZ = 26; EEREEL = 27; EELEER = 28;
EZEEEZ = 29; EREEEL = 30; ELEEER = 31;
ZEEEEZ = 32; REEEEL = 33; LEEEER = 34;
EEEZZE = 35; EEERLE = 36; EEELRE = 37;
EEZEZE = 38; EERELE = 39; EELERE = 40;
EZEEZE = 41; EREELE = 42; ELEERE = 43;
ZEEEZE = 44; REEELE = 45; LEEERE = 46;
EEZZEE = 47; EERLEE = 48; EELREE = 49;
EZEZEE = 50; ERELEE = 51; ELEREE = 52;
ZEEZEE = 53; REELEE = 54; LEEREE = 55;
EZZEEE = 56; ERLEEE = 57; ELREEE = 58;
ZEZEEE = 59; RELEEE = 60; LEREEE = 61;
ZZEEEE = 62; RLEEEE = 63; LREEEE = 64;
% ZR ZL RZ LZ------------------
EEEEZR = 65; EEEEZL = 66; EEEERZ = 67; EEEELZ = 68;
EEEZER = 69; EEEZEL = 70; EEEREZ = 71; EEELEZ = 72;
EEZEER = 73; EEZEEL = 74; EEREEZ = 75; EELEEZ = 76;
EZEEER = 77; EZEEEL = 78; EREEEZ = 79; ELEEEZ = 80;
ZEEEER = 81; ZEEEEL = 82; REEEEZ = 83; LEEEEZ = 84;
EEEZRE = 85; EEEZLE = 86; EEERZE = 87; EEELZE = 88;
EEZERE = 89; EEZELE = 90; EEREZE = 91; EELEZE = 92;
EZEERE = 93; EZEELE = 94; EREEZE = 95; ELEEZE = 96;
ZEEERE = 97; ZEEELE = 98; REEEZE = 99; LEEEZE = 100;
EEZREE = 101; EEZLEE = 102; EERZEE = 103; EELZEE = 104;
EZEREE = 105; EZELEE = 106; EREZEE = 107; ELEZEE = 108;
ZEEREE = 109; ZEELEE = 110; REEZEE = 111; LEEZEE = 112;
EZREEE = 113; EZLEEE = 114; ERZEEE = 115; ELZEEE = 116;
ZEREEE = 117; ZELEEE = 118; REZEEE = 119; LEZEEE = 120;
ZREEEE = 121; ZLEEEE = 122; RZEEEE = 123; LZEEEE = 124;
% RR LL ------------------
EEEERR = 125; EEEELL = 126;
EEERER = 127; EEELEL = 128;
EEREER = 129; EELEEL = 130;
EREEER = 131; ELEEEL = 132;
REEEER = 133; LEEEEL = 134;
EEERRE = 135; EEELLE = 136;
EERERE = 137; EELELE = 138;
EREERE = 139; ELEELE = 140;
REEERE = 141; LEEELE = 142;
EERREE = 143; EELLEE = 144;
EREREE = 145; ELELEE = 146;
REEREE = 147; LEELEE = 148;
ERREEE = 149; ELLEEE = 150;
REREEE = 151; LELEEE = 152;
RREEEE = 153; LLEEEE = 154;
switch iSpin
case 1
switch jSpin
case 6, IJ = [ZEEEEZ REEEEL LEEEER ZEEEER ZEEEEL REEEEZ LEEEEZ REEEER LEEEEL]; % OEEEEO
case 5, IJ = [ZEEEZE REEELE LEEERE ZEEERE ZEEELE REEEZE LEEEZE REEERE LEEELE]; % OEEEOE
case 4, IJ = [ZEEZEE REELEE LEEREE ZEEREE ZEELEE REEZEE LEEZEE REEREE LEELEE]; % OEEOEE
case 3, IJ = [ZEZEEE RELEEE LEREEE ZEREEE ZELEEE REZEEE LEZEEE REREEE LELEEE]; % OEOEEE
case 2, IJ = [ZZEEEE RLEEEE LREEEE ZREEEE ZLEEEE RZEEEE LZEEEE RREEEE LLEEEE]; % OOEEEE
end
case 2
switch jSpin
case 6, IJ = [EZEEEZ EREEEL ELEEER EZEEER EZEEEL EREEEZ ELEEEZ EREEER ELEEEL]; % EOEEEO
case 5, IJ = [EZEEZE EREELE ELEERE EZEERE EZEELE EREEZE ELEEZE EREERE ELEELE]; % EOEEOE
case 4, IJ = [EZEZEE ERELEE ELEREE EZEREE EZELEE EREZEE ELEZEE EREREE ELELEE]; % EOEOEE
case 3, IJ = [EZZEEE ERLEEE ELREEE EZREEE EZLEEE ERZEEE ELZEEE ERREEE ELLEEE]; % EOOEEE
end
case 3
switch jSpin
case 6, IJ = [EEZEEZ EEREEL EELEER EEZEER EEZEEL EEREEZ EELEEZ EEREER EELEEL]; % EEOEEO
case 5, IJ = [EEZEZE EERELE EELERE EEZERE EEZELE EEREZE EELEZE EERERE EELELE]; % EEOEOE
case 4, IJ = [EEZZEE EERLEE EELREE EEZREE EEZLEE EERZEE EELZEE EERREE EELLEE]; % EEOOEE
end
case 4
switch jSpin
case 6, IJ = [EEEZEZ EEEREL EEELER EEEZER EEEZEL EEEREZ EEELEZ EEERER EEELEL]; % EEEOEO
case 5, IJ = [EEEZZE EEERLE EEELRE EEEZRE EEEZLE EEERZE EEELZE EEERRE EEELLE]; % EEEOOE
end
case 5, IJ = [EEEEZZ EEEERL EEEELR EEEEZR EEEEZL EEEERZ EEEELZ EEEERR EEEELL]; % EEEEOO
end
end
% 1 2 3 4 5 6 7 8 9
% [ZZ RL LR ZR ZL RZ LZ RR LL]
zz = IJ(1);
rl = IJ(2); lr = IJ(3);
zr = IJ(4); zl = IJ(5);
rz = IJ(6); lz = IJ(7);
rr = IJ(8); ll = IJ(9);
end
function test_spinopidx2()
for clusterSize = 2:6
for iSpin = 1:clusterSize-1
for jSpin = iSpin+1:clusterSize
[zz0,rl0,lr0,zr0,zl0,rz0,lz0,rr0,ll0] = ...
spinopidx2_v0(clusterSize,iSpin,jSpin);
zrl0 = [zz0,rl0,lr0,zr0,zl0,rz0,lz0,rr0,ll0];
[zz,rl,lr,zr,zl,rz,lz,rr,ll] = spinopidx2(clusterSize,iSpin,jSpin);
zrl1 = [zz,rl,lr,zr,zl,rz,lz,rr,ll];
if(max( abs(zrl1-zrl0) )>0)
fprintf(['\n\nError in spinopidx2(): ', ...
'for cluster size %d, double spin indices are \n'],clusterSize);
disp(zrl1)
disp('when they should be');
disp(zrl0)
error('Error above.');
end
end
end
end
end
function [xx,xy,xz,yx,yy,yz,zx,zy,zz] = spinopidx_nq(iSpin,SpinXiXjOp)
% ENUM for spin-operator indices.
XX_ = 1; XY_ = 4; XZ_ = 7;
YX_ = 2; YY_ = 5; YZ_ = 8;
ZX_ = 3; ZY_ = 6; ZZ_ = 9;
if size(SpinXiXjOp,3)==9
off = 0;
else
off = (iSpin-1)*9;
end
xx = XX_ + off;
xy = XY_ + off;
xz = XZ_ + off;
yx = YX_ + off;
yy = YY_ + off;
yz = YZ_ + off;
zx = ZX_ + off;
zy = ZY_ + off;
zz = ZZ_ + off;
end
function test_spinops(SpinOp,clusterSize)
for iSpin = 1:clusterSize
[ze,pe,me] = spinopidx(clusterSize,iSpin);
for jSpin = iSpin+1:clusterSize
[ez,ep,em] = spinopidx(clusterSize,jSpin);
[zz,rl,lr,zr,zl,rz,lz,~,~] = spinopidx2(clusterSize,iSpin,jSpin);
assert(max(max(abs( ...
SpinOp(:,:,ze) - 2*commutator(SpinOp(:,:,rz),SpinOp(:,:,lz) ) ...
)))==0);
assert(max(max(abs( ...
SpinOp(:,:,ez) - 2*commutator(SpinOp(:,:,zr),SpinOp(:,:,zl) ) ...
)))==0);
assert(max(max(abs( ...
2*SpinOp(:,:,ze) - commutator(SpinOp(:,:,pe),SpinOp(:,:,me) ) ...
) ))==0);
assert(max(max(abs( ...
2*SpinOp(:,:,ez) - commutator(SpinOp(:,:,ep),SpinOp(:,:,em) ) ...
) ))==0);
assert(max(max(abs( ...
SpinOp(:,:,zz) -SpinOp(:,:,ze)*SpinOp(:,:,ez) ...
)))==0);
assert(max(max(abs( ...
SpinOp(:,:,rl) -SpinOp(:,:,pe)*SpinOp(:,:,em) ...
)))==0)
assert(max(max(abs( ...
SpinOp(:,:,lr) -SpinOp(:,:,ep)*SpinOp(:,:,me) ...
)))==0)
assert(max(max(abs( ...
SpinOp(:,:,ep) -SpinOp(:,:,pe) ...
))) ~=0 );
assert(max(max(abs( ...
SpinOp(:,:,em) -SpinOp(:,:,me) ...
))) ~=0 );
assert(max(max(abs( ...
SpinOp(:,:,ez) -SpinOp(:,:,ze) ...
))) ~=0 );
end
end
end
%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
%<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
function C = commutator(A,B)
C = A*B - B*A;
end
%>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>