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getOpNames.m
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getOpNames.m
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%==========================================================================
% Generate a list of strings specifying the cluster spin-operator.
%==========================================================================
function opNames = getOpNames(clusterSize)
% Get number of operators for the given cluster size.
numOps = 1 + 3*clusterSize + 9*NchooseK(clusterSize,2);
% Initialize output.
opNames = cell(1,numOps);
% Begin the identity string.
opNames{1} = 'E';
% Get the 1 identity operator EE....EE.
for iSpin = 2:clusterSize
opNames{1} = [opNames{1},'E'];
end
% Set index.
idx = 1;
Op = {'Z','R','L'};
% Add 3*clusterSize operators of the form EE...O...EE,
% where O in {Z,R,L}.
% Loop over spins.
for iSpin = 1:clusterSize
% Adjust for placement order.
ispin_index = clusterSize-iSpin + 1;
% Loop over the operator set indices.
for iop = 1:3
idx = idx + 1;
% Initialize operator string with the identity string.
opNames{idx} = opNames{1};
% Set the non-identity element.
opNames{idx}(ispin_index) = Op{iop};
end
end
OpOp = {'ZZ','RL','LR'};
% Add 3*NchooseK(clusterSize,2) operators of the form EE...O1...E...O2...EE,
% where O1,2 in OpOp{}(1,2).
% Loop over spins.
for jSpin = 1:clusterSize-1
% Adjust for placement order.
jspin_index = clusterSize-jSpin + 1;
% Loop over spins.
for iSpin = jSpin+1:clusterSize
% Adjust for placement order.
ispin_index = clusterSize-iSpin + 1;
% Loop over the operator set indices.
for iop = 1:3
% Increment index.
idx = idx + 1;
% Initialize operator string with the identity string.
opNames{idx} = opNames{1};
% Set the non-identity elements.
opNames{idx}(ispin_index) = OpOp{iop}(1);
opNames{idx}(jspin_index) = OpOp{iop}(2);
end
end
end
%
Op_CD = {'ZR', 'ZL', 'RZ', 'LZ'};
% Add 4*NchooseK(clusterSize,2) operators of the form EE...O1...E...O2...EE,
% where O1,2 in Op_CD{}(1,2).
% Loop over spins.
for jSpin = 1:clusterSize-1
% Adjust for placement order.
jspin_index = clusterSize-jSpin + 1;
% Loop over spins.
for iSpin = jSpin+1:clusterSize
% Adjust for placement order.
ispin_index = clusterSize-iSpin + 1;
% Loop over the operator set indices.
for iop = 1:4
% Increment index.
idx = idx + 1;
% Initialize operator string with the identity string.
opNames{idx} = opNames{1};
% Set the non-identity elements.
opNames{idx}(ispin_index) = Op_CD{iop}(1);
opNames{idx}(jspin_index) = Op_CD{iop}(2);
end
end
end
% RR and LL
% Add 4*NchooseK(clusterSize,2) operators of the form EE...O...E...O...EE,
% where O1,2 in {R,L}.
% Loop over spins.
for jSpin = 1:clusterSize-1
% Adjust for placement order.
jspin_index = clusterSize-jSpin + 1;
% Loop over spins.
for iSpin = jSpin+1:clusterSize
% Adjust for placement order.
ispin_index = clusterSize-iSpin + 1;
% Loop over the operator set indices.
for iop = 2:3
% Increment index.
idx = idx + 1;
% Initialize operator string with the identity string.
opNames{idx} = opNames{1};
% Set the non-identity elements.
opNames{idx}(ispin_index) = Op{iop};
opNames{idx}(jspin_index) = Op{iop};
end
end
end
end
% Information on Operator Indices
%--------------------------------------------------------------------------
% 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 +- -+
% OO (11-14): z+ z- +z -z
% OO (15-16): ++ --
%--------------------------------------------------------------------------
% 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
% EEE = 1;
% EEZ = 2; EER = 3; EEL = 4;
% EZE = 5; ERE = 6; ELE = 7;
% ZEE = 8; REE = 9; LEE = 10;
% EZZ = 11; ERL = 12; ELR = 13;
% ZEZ = 14; REL = 15; LER = 16;
% ZZE = 17; RLE = 18; LRE = 19;
%
% EZR = 20; EZL = 21; ERZ = 22; ELZ = 23;
% ZER = 24; ZEL = 25; REZ = 26; LEZ = 27;
% ZRE = 28; ZLE = 29; RZE = 30; LZE = 31;
%
% ERR = 32; ELL = 33;
% RER = 34; LEL = 35;
% RRE = 36; LLE = 37;
%--------------------------------------------------------------------------
% 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
% 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;
% 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;
%
%
% EEZR = 31; EEZL = 32; EERZ = 33; EELZ = 34;
% EZER = 35; EZEL = 36; EREZ = 37; ELEZ = 38;
% ZEER = 39; ZEEL = 40; REEZ = 41; LEEZ = 42;
% EZRE = 43; EZLE = 44; ERZE = 45; ELZE = 46;
% ZERE = 47; ZELE = 48; REZE = 49; LEZE = 50;
% ZREE = 51; ZLEE = 52; RZEE = 53; LZEE = 54;
%
% EERR = 55; EELL = 56;
% ERER = 57; ELEL = 58;
% REER = 59; LEEL = 60;
% ERRE = 61; ELLE = 62;
% RERE = 63; LELE = 64;
% RREE = 65; LLEE = 66;
%--------------------------------------------------------------------------
% 5-Clusters: EEEEE EEEEO EEEOE EEOEE EOEEE OEEEE EEEOO EEOEO EOEEO OEEEO
% EEOOE EOEOE OEEOE EOOEE OEOEE OOEEE
%--------------------------------------------------------------------------
% 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
%--------------------------------------------------------------------------
% 6-Clusters: EEEEEE EEEEEO EEEEOE EEEOEE EEOEEE EOEEEE OEEEEE EEEEOO
% EEEOEO EEOEEO EOEEEO OEEEEO EEEOOE EEOEOE EOEEOE OEEEOE EEOOEE EOEOEE OEEOEE EOOEEE OOEEEE
%--------------------------------------------------------------------------
% 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
%--------------------------------------------------------------------------
% 7-Clusters:
%--------------------------------------------------------------------------
% EEEEEEE (1) : EEEEEEE
% EEEEEEO (2-4) : EEEEEEz EEEEEE+ EEEEEE-
% EEEEEOE (5-7) : EEEEEzE EEEEE+E EEEEE-E
% EEEEOEE (8-10) : EEEEzEE EEEE+EE EEEE-EE
% EEEOEEE (11-13): EEEzEEE EEE+EEE EEE-EEE
% EEOEEEE (14-19): EEzEEEE EE+EEEE EE-EEEE
% EOEEEEE (17-22): EzEEEEE E+EEEEE E-EEEEE
% OEEEEEE (20-25): zEEEEEE +EEEEEE -EEEEEE
% EEEEEOO (20-28): EEEEEzz EEEEE+- EEEEE-+
% EEEEOEO (23-31): EEEEzEz EEEE+E- EEEE-E+
% EEEOEEO (26-34): EEEzEEz EEE+EE- EEE-EE+
% EEOEEEO (29-37): EEzEEEz EE+EEE- EE-EEE+
% EOEEEEO (32-40): EzEEEEz E+EEEE- E-EEEE+
% OEEEEEO (32-43): zEEEEEz +EEEEE- -EEEEE+
% EEEEOOE (35-46): EEEEzzE EEEE+-E EEEE-+E
% EEEOEOE (38-49): EEEzEzE EEE+E-E EEE-E+E
% EEOEEOE (41-52): EEzEEzE EE+EE-E EE-EE+E
% EOEEEOE (44-55): EzEEEzE E+EEE-E E-EEE+E
% OEEEEOE (44-58): zEEEEzE +EEEE-E -EEEE+E
% EEEOOEE (47-61): EEEzzEE EEE+-EE EEE-+EE
% EEOEOEE (50-64): EEzEzEE EE+E-EE EE-E+EE
% EOEEOEE (53-67): EzEEzEE E+EE-EE E-EE+EE
% OEEEOEE (53-70): zEEEzEE +EEE-EE -EEE+EE
% EEOOEEE (56-73): EEzzEEE EE+-EEE EE-+EEE
% EOEOEEE (59-76): EzEzEEE E+E-EEE E-E+EEE
% OEEOEEE (59-79): zEEzEEE +EE-EEE -E+EEE
% EOOEEEE (62-82): EzzEEEE E+-EEEE E-+EEEE
% OEOEEEE (62-85): zEzEEEE +E-EEEE -E+EEEE
% OOEEEEE (62-88): zzEEEEE +-EEEEE -+EEEEE
%--------------------------------------------------------------------------
% 8-Clusters:
%--------------------------------------------------------------------------
% EEEEEEEE (1) : EEEEEEE
% EEEEEEEO (2-4) : EEEEEEz EEEEEE+ EEEEEE-
% EEEEEEOE (5-7) : EEEEEzE EEEEE+E EEEEE-E
% EEEEEOEE (8-10) : EEEEzEE EEEE+EE EEEE-EE
% EEEEOEEE (11-13): EEEzEEE EEE+EEE EEE-EEE
% EEEOEEEE (14-16): EEzEEEE EE+EEEE EE-EEEE
% EEOEEEEE (17-19): EzEEEEE E+EEEEE E-EEEEE
% EOEEEEEE (17-19): zEEEEEE +EEEEEE -EEEEEE
% OEEEEEEE (17-19): zEEEEEE +EEEEEE -EEEEEE
% EEEEEEOO (20-22): EEEEEzz EEEEE+- EEEEE-+
% EEEEEOEO (23-25): EEEEzEz EEEE+E- EEEE-E+
% EEEEOEEO (26-28): EEEzEEz EEE+EE- EEE-EE+
% EEEOEEEO (29-31): EEzEEEz EE+EEE- EE-EEE+
% EEOEEEEO (32-34): EzEEEEz E+EEEE- E-EEEE+
% EOEEEEEO (32-34): zEEEEEz +EEEEE- -EEEEE+
% OEEEEEEO (32-34): zEEEEEz +EEEEE- -EEEEE+
% EEEEEOOE (35-37): EEEEzzE EEEE+-E EEEE-+E
% EEEEOEOE (38-40): EEEzEzE EEE+E-E EEE-E+E
% EEEOEEOE (41-43): EEzEEzE EE+EE-E EE-EE+E
% EEOEEEOE (44-46): EzEEEzE E+EEE-E E-EEE+E
% EOEEEEOE (44-46): zEEEEzE +EEEE-E -EEEE+E
% EOEEEEOE (44-46): zEEEEzE +EEEE-E -EEEE+E
% OEEEEEOE (44-46): zEEEEzE +EEEE-E -EEEE+E
% EEEEOOEE (47-49): EEEzzEE EEE+-EE EEE-+EE
% EEEOEOEE (50-51): EEzEzEE EE+E-EE EE-E+EE
% EEOEEOEE (53-55): EzEEzEE E+EE-EE E-EE+EE
% EOEEEOEE (53-55): zEEEzEE +EEE-EE -EEE+EE
% OEEEEOEE (53-55): zEEEzEE +EEE-EE -EEE+EE
% EEEOOEEE (56-58): EEzzEEE EE+-EEE EE-+EEE
% EEOEOEEE (59-61): EzEzEEE E+E-EEE E-E+EEE
% EOEEOEEE (59-61): zEEzEEE +EE-EEE -E+EEE
% OEEEOEEE (59-61): zEEzEEE +EE-EEE -E+EEE
% EEOOEEEE (62-64): EzzEEEE E+-EEEE E-+EEEE
% EOEOEEEE (62-64): zEzEEEE +E-EEEE -E+EEEE
% OEEOEEEE (62-64): zEzEEEE +E-EEEE -E+EEEE
% EOOEEEEE (62-64): zzEEEEE +-EEEEE -+EEEEE
% OEOEEEEE (62-64): zzEEEEE +-EEEEE -+EEEEE
% OOEEEEEE (62-112): zzEEEEE +-EEEEE -+EEEEE