幺正变换

ClearAll["`*"];
{s0,sx,sy,sz}=PauliMatrix[{0,1,2,3}];
g1=KroneckerProduct[sz,sz];(*fFIM*)
g2=KroneckerProduct[sz,sy];(*SOC*)
g3=KroneckerProduct[sy,sy];(*pairing*)
g4=KroneckerProduct[sz,s0];(*mu*)
ham=d1 g1+d2 g2+d3 g3-d4 g4;
U0=KroneckerProduct[(sz+s0)/2,s0]+KroneckerProduct[(s0-sz)/2,-I sy];
Style[MatrixForm[U0],FontSize->24,Blue]
func1[mat_]:=Style[MatrixForm[U0.mat.Inverse[U0]],FontSize->20,Blue]
Style[MatrixForm[#],FontSize->20,Red]&/@{KroneckerProduct[sz,sz],KroneckerProduct[sz,sy],KroneckerProduct[sy,sy],KroneckerProduct[sz,s0]}(*Particle-hole * Spin*)
func1[#]&/@{g1,g2,g3,g4}

Style[MatrixForm[#],FontSize->20,Green]&/@{KroneckerProduct[s0,sz],KroneckerProduct[sz,sy],KroneckerProduct[sx,s0],KroneckerProduct[sz,s0]}(*Particle-hole * Spin*)

能带对比

ClearAll["`*"];
{s0,sx,sy,sz}=PauliMatrix[{0,1,2,3}];
g1=KroneckerProduct[sz,sz];
g2=KroneckerProduct[sz,sy];
g3=KroneckerProduct[sy,sy];
g4=KroneckerProduct[sz,s0];
ham1=d1 g1+d2 g2+d3 g3-d4 g4;
vals1=Eigenvalues[ham1]//FullSimplify
vals1=  vals1/.{d1->(V0+V1 Cos[k]),d2->λ0 Sin[k],d3->Δ0,d4->μ};
gg1=KroneckerProduct[s0,sz];
gg2=KroneckerProduct[sz,sy];
gg3=KroneckerProduct[sx,s0];
gg4=KroneckerProduct[sz,s0];
ham2=d1 gg1+d2 gg2+d3 gg3-d4 gg4;
vals2=Eigenvalues[ham2]//FullSimplify
vals2=  vals2/.{d1->(V0+V1 Cos[k]),d2->λ0 Sin[k],d3->Δ0,d4->μ};
(*{V0,V1,λ0,Δ0,μ}={1.0,1.0,1.0,0.5,0.2};
Plot[{vals1,vals2},{k,-Pi,Pi},PlotRange->All,ImageSize->Large]*)

vals1/.{k->0}//FullSimplify
vals1/.{k->Pi}//FullSimplify