GellMann1 = [0 1 0; 1 0 0; 0 0 0];
GellMann2 = [0 -1i 0; 1i 0 0; 0 0 0];
GellMann3 = [1 0 0; 0 -1 0; 0 0 0];
GellMann4 = [0 0 1; 0 0 0; 1 0 0];
GellMann5 = [0 0 -1i; 0 0 0; 1i 0 0];
GellMann6 = [0 0 0; 0 0 1; 0 1 0];
GellMann7 = [0 0 0; 0 0 -1i; 0 1i 0];
GellMann8 = [1/sqrt(3) 0 0; 0 1/sqrt(3) 0; 0 0 -2/sqrt(3) ];
normtheta= sqrt(theta1^2 + theta2^2 + theta3^2 + theta4^2 + theta5^2 + theta6^2 + theta6^2 + theta8^2);
PhaseMatrix = theta1*GellMann1 + theta2*GellMann2 + theta3*GellMann3 + theta4*GellMann4 + theta5*GellMann5 + theta6*GellMann6+ theta7*GellMann7 + theta8*GellMann8 ;
counter_Eigenvalues1_vector =1;
counter_Eigenvalues2_vector =1;
counter_Eigenvalues3_vector =1;
for k = -2*pi : 4*pi/500 : 2*pi
fprintf('The corresponding k is %d \n', k);
Hamiltonian= J*(expm(1i*(k*eye(3) - PhaseMatrix)) + expm(-1i*(k*eye(3) - PhaseMatrix)));
eig_Correct = eig(Hamiltonian);
e1correct = eig_Correct(1);
e2correct = eig_Correct(2);
e3correct = eig_Correct(3);
Eigenvalues1_vector(1, counter_Eigenvalues1_vector) = (e1correct);
counter_Eigenvalues1_vector = counter_Eigenvalues1_vector +1;
Eigenvalues2_vector(1, counter_Eigenvalues2_vector) = (e2correct);
counter_Eigenvalues2_vector = counter_Eigenvalues2_vector +1;
Eigenvalues3_vector(1, counter_Eigenvalues3_vector) = (e3correct);
counter_Eigenvalues3_vector = counter_Eigenvalues3_vector +1;
end
The corresponding k is -6.283185e+00
The corresponding k is -6.258053e+00
The corresponding k is -6.232920e+00
The corresponding k is -6.207787e+00
The corresponding k is -6.182654e+00
The corresponding k is -6.157522e+00
The corresponding k is -6.132389e+00
The corresponding k is -6.107256e+00
The corresponding k is -6.082123e+00
The corresponding k is -6.056991e+00
The corresponding k is -6.031858e+00
The corresponding k is -6.006725e+00
The corresponding k is -5.981592e+00
The corresponding k is -5.956460e+00
The corresponding k is -5.931327e+00
The corresponding k is -5.906194e+00
The corresponding k is -5.881061e+00
The corresponding k is -5.855929e+00
The corresponding k is -5.830796e+00
The corresponding k is -5.805663e+00
The corresponding k is -5.780530e+00
The corresponding k is -5.755398e+00
The corresponding k is -5.730265e+00
The corresponding k is -5.705132e+00
The corresponding k is -5.680000e+00
The corresponding k is -5.654867e+00
The corresponding k is -5.629734e+00
The corresponding k is -5.604601e+00
The corresponding k is -5.579469e+00
The corresponding k is -5.554336e+00
The corresponding k is -5.529203e+00
The corresponding k is -5.504070e+00
The corresponding k is -5.478938e+00
The corresponding k is -5.453805e+00
The corresponding k is -5.428672e+00
The corresponding k is -5.403539e+00
The corresponding k is -5.378407e+00
The corresponding k is -5.353274e+00
The corresponding k is -5.328141e+00
The corresponding k is -5.303008e+00
The corresponding k is -5.277876e+00
The corresponding k is -5.252743e+00
The corresponding k is -5.227610e+00
The corresponding k is -5.202477e+00
The corresponding k is -5.177345e+00
The corresponding k is -5.152212e+00
The corresponding k is -5.127079e+00
The corresponding k is -5.101946e+00
The corresponding k is -5.076814e+00
The corresponding k is -5.051681e+00
The corresponding k is -5.026548e+00
The corresponding k is -5.001416e+00
The corresponding k is -4.976283e+00
The corresponding k is -4.951150e+00
The corresponding k is -4.926017e+00
The corresponding k is -4.900885e+00
The corresponding k is -4.875752e+00
The corresponding k is -4.850619e+00
The corresponding k is -4.825486e+00
The corresponding k is -4.800354e+00
The corresponding k is -4.775221e+00
The corresponding k is -4.750088e+00
The corresponding k is -4.724955e+00
The corresponding k is -4.699823e+00
The corresponding k is -4.674690e+00
The corresponding k is -4.649557e+00
The corresponding k is -4.624424e+00
The corresponding k is -4.599292e+00
The corresponding k is -4.574159e+00
The corresponding k is -4.549026e+00
The corresponding k is -4.523893e+00
The corresponding k is -4.498761e+00
The corresponding k is -4.473628e+00
The corresponding k is -4.448495e+00
The corresponding k is -4.423362e+00
The corresponding k is -4.398230e+00
The corresponding k is -4.373097e+00
The corresponding k is -4.347964e+00
The corresponding k is -4.322831e+00
The corresponding k is -4.297699e+00
The corresponding k is -4.272566e+00
The corresponding k is -4.247433e+00
The corresponding k is -4.222301e+00
The corresponding k is -4.197168e+00
The corresponding k is -4.172035e+00
The corresponding k is -4.146902e+00
The corresponding k is -4.121770e+00
The corresponding k is -4.096637e+00
The corresponding k is -4.071504e+00
The corresponding k is -4.046371e+00
The corresponding k is -4.021239e+00
The corresponding k is -3.996106e+00
The corresponding k is -3.970973e+00
The corresponding k is -3.945840e+00
The corresponding k is -3.920708e+00
The corresponding k is -3.895575e+00
The corresponding k is -3.870442e+00
The corresponding k is -3.845309e+00
The corresponding k is -3.820177e+00
The corresponding k is -3.795044e+00
The corresponding k is -3.769911e+00
The corresponding k is -3.744778e+00
The corresponding k is -3.719646e+00
The corresponding k is -3.694513e+00
The corresponding k is -3.669380e+00
The corresponding k is -3.644247e+00
The corresponding k is -3.619115e+00
The corresponding k is -3.593982e+00
The corresponding k is -3.568849e+00
The corresponding k is -3.543717e+00
The corresponding k is -3.518584e+00
The corresponding k is -3.493451e+00
The corresponding k is -3.468318e+00
The corresponding k is -3.443186e+00
The corresponding k is -3.418053e+00
The corresponding k is -3.392920e+00
The corresponding k is -3.367787e+00
The corresponding k is -3.342655e+00
The corresponding k is -3.317522e+00
The corresponding k is -3.292389e+00
The corresponding k is -3.267256e+00
The corresponding k is -3.242124e+00
The corresponding k is -3.216991e+00
The corresponding k is -3.191858e+00
The corresponding k is -3.166725e+00
The corresponding k is -3.141593e+00
The corresponding k is -3.116460e+00
The corresponding k is -3.091327e+00
The corresponding k is -3.066194e+00
The corresponding k is -3.041062e+00
The corresponding k is -3.015929e+00
The corresponding k is -2.990796e+00
The corresponding k is -2.965663e+00
The corresponding k is -2.940531e+00
The corresponding k is -2.915398e+00
The corresponding k is -2.890265e+00
The corresponding k is -2.865133e+00
The corresponding k is -2.840000e+00
The corresponding k is -2.814867e+00
The corresponding k is -2.789734e+00
The corresponding k is -2.764602e+00
The corresponding k is -2.739469e+00
The corresponding k is -2.714336e+00
The corresponding k is -2.689203e+00
The corresponding k is -2.664071e+00
The corresponding k is -2.638938e+00
The corresponding k is -2.613805e+00
The corresponding k is -2.588672e+00
The corresponding k is -2.563540e+00
The corresponding k is -2.538407e+00
The corresponding k is -2.513274e+00
The corresponding k is -2.488141e+00
The corresponding k is -2.463009e+00
The corresponding k is -2.437876e+00
The corresponding k is -2.412743e+00
The corresponding k is -2.387610e+00
The corresponding k is -2.362478e+00
The corresponding k is -2.337345e+00
The corresponding k is -2.312212e+00
The corresponding k is -2.287079e+00
The corresponding k is -2.261947e+00
The corresponding k is -2.236814e+00
The corresponding k is -2.211681e+00
The corresponding k is -2.186548e+00
The corresponding k is -2.161416e+00
The corresponding k is -2.136283e+00
The corresponding k is -2.111150e+00
The corresponding k is -2.086018e+00
The corresponding k is -2.060885e+00
The corresponding k is -2.035752e+00
The corresponding k is -2.010619e+00
The corresponding k is -1.985487e+00
The corresponding k is -1.960354e+00
The corresponding k is -1.935221e+00
The corresponding k is -1.910088e+00
The corresponding k is -1.884956e+00
The corresponding k is -1.859823e+00
The corresponding k is -1.834690e+00
The corresponding k is -1.809557e+00
The corresponding k is -1.784425e+00
The corresponding k is -1.759292e+00
The corresponding k is -1.734159e+00
The corresponding k is -1.709026e+00
The corresponding k is -1.683894e+00
The corresponding k is -1.658761e+00
The corresponding k is -1.633628e+00
The corresponding k is -1.608495e+00
The corresponding k is -1.583363e+00
The corresponding k is -1.558230e+00
The corresponding k is -1.533097e+00
The corresponding k is -1.507964e+00
The corresponding k is -1.482832e+00
The corresponding k is -1.457699e+00
The corresponding k is -1.432566e+00
The corresponding k is -1.407434e+00
The corresponding k is -1.382301e+00
The corresponding k is -1.357168e+00
The corresponding k is -1.332035e+00
The corresponding k is -1.306903e+00
The corresponding k is -1.281770e+00
The corresponding k is -1.256637e+00
The corresponding k is -1.231504e+00
The corresponding k is -1.206372e+00
The corresponding k is -1.181239e+00
The corresponding k is -1.156106e+00
The corresponding k is -1.130973e+00
The corresponding k is -1.105841e+00
The corresponding k is -1.080708e+00
The corresponding k is -1.055575e+00
The corresponding k is -1.030442e+00
The corresponding k is -1.005310e+00
The corresponding k is -9.801769e-01
The corresponding k is -9.550442e-01
The corresponding k is -9.299114e-01
The corresponding k is -9.047787e-01
The corresponding k is -8.796459e-01
The corresponding k is -8.545132e-01
The corresponding k is -8.293805e-01
The corresponding k is -8.042477e-01
The corresponding k is -7.791150e-01
The corresponding k is -7.539822e-01
The corresponding k is -7.288495e-01
The corresponding k is -7.037168e-01
The corresponding k is -6.785840e-01
The corresponding k is -6.534513e-01
The corresponding k is -6.283185e-01
The corresponding k is -6.031858e-01
The corresponding k is -5.780530e-01
The corresponding k is -5.529203e-01
The corresponding k is -5.277876e-01
The corresponding k is -5.026548e-01
The corresponding k is -4.775221e-01
The corresponding k is -4.523893e-01
The corresponding k is -4.272566e-01
The corresponding k is -4.021239e-01
The corresponding k is -3.769911e-01
The corresponding k is -3.518584e-01
The corresponding k is -3.267256e-01
The corresponding k is -3.015929e-01
The corresponding k is -2.764602e-01
The corresponding k is -2.513274e-01
The corresponding k is -2.261947e-01
The corresponding k is -2.010619e-01
The corresponding k is -1.759292e-01
The corresponding k is -1.507964e-01
The corresponding k is -1.256637e-01
The corresponding k is -1.005310e-01
The corresponding k is -7.539822e-02
The corresponding k is -5.026548e-02
The corresponding k is -2.513274e-02
The corresponding k is 0
The corresponding k is 2.513274e-02
The corresponding k is 5.026548e-02
The corresponding k is 7.539822e-02
The corresponding k is 1.005310e-01
The corresponding k is 1.256637e-01
The corresponding k is 1.507964e-01
The corresponding k is 1.759292e-01
The corresponding k is 2.010619e-01
The corresponding k is 2.261947e-01
The corresponding k is 2.513274e-01
The corresponding k is 2.764602e-01
The corresponding k is 3.015929e-01
The corresponding k is 3.267256e-01
The corresponding k is 3.518584e-01
The corresponding k is 3.769911e-01
The corresponding k is 4.021239e-01
The corresponding k is 4.272566e-01
The corresponding k is 4.523893e-01
The corresponding k is 4.775221e-01
The corresponding k is 5.026548e-01
The corresponding k is 5.277876e-01
The corresponding k is 5.529203e-01
The corresponding k is 5.780530e-01
The corresponding k is 6.031858e-01
The corresponding k is 6.283185e-01
The corresponding k is 6.534513e-01
The corresponding k is 6.785840e-01
The corresponding k is 7.037168e-01
The corresponding k is 7.288495e-01
The corresponding k is 7.539822e-01
The corresponding k is 7.791150e-01
The corresponding k is 8.042477e-01
The corresponding k is 8.293805e-01
The corresponding k is 8.545132e-01
The corresponding k is 8.796459e-01
The corresponding k is 9.047787e-01
The corresponding k is 9.299114e-01
The corresponding k is 9.550442e-01
The corresponding k is 9.801769e-01
The corresponding k is 1.005310e+00
The corresponding k is 1.030442e+00
The corresponding k is 1.055575e+00
The corresponding k is 1.080708e+00
The corresponding k is 1.105841e+00
The corresponding k is 1.130973e+00
The corresponding k is 1.156106e+00
The corresponding k is 1.181239e+00
The corresponding k is 1.206372e+00
The corresponding k is 1.231504e+00
The corresponding k is 1.256637e+00
The corresponding k is 1.281770e+00
The corresponding k is 1.306903e+00
The corresponding k is 1.332035e+00
The corresponding k is 1.357168e+00
The corresponding k is 1.382301e+00
The corresponding k is 1.407434e+00
The corresponding k is 1.432566e+00
The corresponding k is 1.457699e+00
The corresponding k is 1.482832e+00
The corresponding k is 1.507964e+00
The corresponding k is 1.533097e+00
The corresponding k is 1.558230e+00
The corresponding k is 1.583363e+00
The corresponding k is 1.608495e+00
The corresponding k is 1.633628e+00
The corresponding k is 1.658761e+00
The corresponding k is 1.683894e+00
The corresponding k is 1.709026e+00
The corresponding k is 1.734159e+00
The corresponding k is 1.759292e+00
The corresponding k is 1.784425e+00
The corresponding k is 1.809557e+00
The corresponding k is 1.834690e+00
The corresponding k is 1.859823e+00
The corresponding k is 1.884956e+00
The corresponding k is 1.910088e+00
The corresponding k is 1.935221e+00
The corresponding k is 1.960354e+00
The corresponding k is 1.985487e+00
The corresponding k is 2.010619e+00
The corresponding k is 2.035752e+00
The corresponding k is 2.060885e+00
The corresponding k is 2.086018e+00
The corresponding k is 2.111150e+00
The corresponding k is 2.136283e+00
The corresponding k is 2.161416e+00
The corresponding k is 2.186548e+00
The corresponding k is 2.211681e+00
The corresponding k is 2.236814e+00
The corresponding k is 2.261947e+00
The corresponding k is 2.287079e+00
The corresponding k is 2.312212e+00
The corresponding k is 2.337345e+00
The corresponding k is 2.362478e+00
The corresponding k is 2.387610e+00
The corresponding k is 2.412743e+00
The corresponding k is 2.437876e+00
The corresponding k is 2.463009e+00
The corresponding k is 2.488141e+00
The corresponding k is 2.513274e+00
The corresponding k is 2.538407e+00
The corresponding k is 2.563540e+00
The corresponding k is 2.588672e+00
The corresponding k is 2.613805e+00
The corresponding k is 2.638938e+00
The corresponding k is 2.664071e+00
The corresponding k is 2.689203e+00
The corresponding k is 2.714336e+00
The corresponding k is 2.739469e+00
The corresponding k is 2.764602e+00
The corresponding k is 2.789734e+00
The corresponding k is 2.814867e+00
The corresponding k is 2.840000e+00
The corresponding k is 2.865133e+00
The corresponding k is 2.890265e+00
The corresponding k is 2.915398e+00
The corresponding k is 2.940531e+00
The corresponding k is 2.965663e+00
The corresponding k is 2.990796e+00
The corresponding k is 3.015929e+00
The corresponding k is 3.041062e+00
The corresponding k is 3.066194e+00
The corresponding k is 3.091327e+00
The corresponding k is 3.116460e+00
The corresponding k is 3.141593e+00
The corresponding k is 3.166725e+00
The corresponding k is 3.191858e+00
The corresponding k is 3.216991e+00
The corresponding k is 3.242124e+00
The corresponding k is 3.267256e+00
The corresponding k is 3.292389e+00
The corresponding k is 3.317522e+00
The corresponding k is 3.342655e+00
The corresponding k is 3.367787e+00
The corresponding k is 3.392920e+00
The corresponding k is 3.418053e+00
The corresponding k is 3.443186e+00
The corresponding k is 3.468318e+00
The corresponding k is 3.493451e+00
The corresponding k is 3.518584e+00
The corresponding k is 3.543717e+00
The corresponding k is 3.568849e+00
The corresponding k is 3.593982e+00
The corresponding k is 3.619115e+00
The corresponding k is 3.644247e+00
The corresponding k is 3.669380e+00
The corresponding k is 3.694513e+00
The corresponding k is 3.719646e+00
The corresponding k is 3.744778e+00
The corresponding k is 3.769911e+00
The corresponding k is 3.795044e+00
The corresponding k is 3.820177e+00
The corresponding k is 3.845309e+00
The corresponding k is 3.870442e+00
The corresponding k is 3.895575e+00
The corresponding k is 3.920708e+00
The corresponding k is 3.945840e+00
The corresponding k is 3.970973e+00
The corresponding k is 3.996106e+00
The corresponding k is 4.021239e+00
The corresponding k is 4.046371e+00
The corresponding k is 4.071504e+00
The corresponding k is 4.096637e+00
The corresponding k is 4.121770e+00
The corresponding k is 4.146902e+00
The corresponding k is 4.172035e+00
The corresponding k is 4.197168e+00
The corresponding k is 4.222301e+00
The corresponding k is 4.247433e+00
The corresponding k is 4.272566e+00
The corresponding k is 4.297699e+00
The corresponding k is 4.322831e+00
The corresponding k is 4.347964e+00
The corresponding k is 4.373097e+00
The corresponding k is 4.398230e+00
The corresponding k is 4.423362e+00
The corresponding k is 4.448495e+00
The corresponding k is 4.473628e+00
The corresponding k is 4.498761e+00
The corresponding k is 4.523893e+00
The corresponding k is 4.549026e+00
The corresponding k is 4.574159e+00
The corresponding k is 4.599292e+00
The corresponding k is 4.624424e+00
The corresponding k is 4.649557e+00
The corresponding k is 4.674690e+00
The corresponding k is 4.699823e+00
The corresponding k is 4.724955e+00
The corresponding k is 4.750088e+00
The corresponding k is 4.775221e+00
The corresponding k is 4.800354e+00
The corresponding k is 4.825486e+00
The corresponding k is 4.850619e+00
The corresponding k is 4.875752e+00
The corresponding k is 4.900885e+00
The corresponding k is 4.926017e+00
The corresponding k is 4.951150e+00
The corresponding k is 4.976283e+00
The corresponding k is 5.001416e+00
The corresponding k is 5.026548e+00
The corresponding k is 5.051681e+00
The corresponding k is 5.076814e+00
The corresponding k is 5.101946e+00
The corresponding k is 5.127079e+00
The corresponding k is 5.152212e+00
The corresponding k is 5.177345e+00
The corresponding k is 5.202477e+00
The corresponding k is 5.227610e+00
The corresponding k is 5.252743e+00
The corresponding k is 5.277876e+00
The corresponding k is 5.303008e+00
The corresponding k is 5.328141e+00
The corresponding k is 5.353274e+00
The corresponding k is 5.378407e+00
The corresponding k is 5.403539e+00
The corresponding k is 5.428672e+00
The corresponding k is 5.453805e+00
The corresponding k is 5.478938e+00
The corresponding k is 5.504070e+00
The corresponding k is 5.529203e+00
The corresponding k is 5.554336e+00
The corresponding k is 5.579469e+00
The corresponding k is 5.604601e+00
The corresponding k is 5.629734e+00
The corresponding k is 5.654867e+00
The corresponding k is 5.680000e+00
The corresponding k is 5.705132e+00
The corresponding k is 5.730265e+00
The corresponding k is 5.755398e+00
The corresponding k is 5.780530e+00
The corresponding k is 5.805663e+00
The corresponding k is 5.830796e+00
The corresponding k is 5.855929e+00
The corresponding k is 5.881061e+00
The corresponding k is 5.906194e+00
The corresponding k is 5.931327e+00
The corresponding k is 5.956460e+00
The corresponding k is 5.981592e+00
The corresponding k is 6.006725e+00
The corresponding k is 6.031858e+00
The corresponding k is 6.056991e+00
The corresponding k is 6.082123e+00
The corresponding k is 6.107256e+00
The corresponding k is 6.132389e+00
The corresponding k is 6.157522e+00
The corresponding k is 6.182654e+00
The corresponding k is 6.207787e+00
The corresponding k is 6.232920e+00
The corresponding k is 6.258053e+00
The corresponding k is 6.283185e+00
k = -2*pi : 4*pi/500 : 2*pi
k =
-6.2832 -6.2581 -6.2329 -6.2078 -6.1827 -6.1575 -6.1324 -6.1073 -6.0821 -6.0570 -6.0319 -6.0067 -5.9816 -5.9565 -5.9313 -5.9062 -5.8811 -5.8559 -5.8308 -5.8057 -5.7805 -5.7554 -5.7303 -5.7051 -5.6800 -5.6549 -5.6297 -5.6046 -5.5795 -5.5543
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
plot(k, Eigenvalues1_vector,k, Eigenvalues2_vector,k,Eigenvalues3_vector)
Warning: Imaginary parts of complex X and/or Y arguments ignored.