In [1]:

    

%pylab inline
import sympy
sympy.init_printing()


    

    




Populating the interactive namespace from numpy and matplotlib

In [8]:

    

def mataf(h):
    'Array flatten a matrix list of appropriate dimensions'
    H=sympy.Matrix.hstack(*h[0])
    for sor in range(1,len(h)):
        H=sympy.Matrix.vstack(H,sympy.Matrix.hstack(*h[sor]))
    return H


    

In [9]:

    

S1=sympy.physics.matrices.msigma(1)
S2=sympy.physics.matrices.msigma(2)
S3=sympy.physics.matrices.msigma(3)
S0=S1*S1
N=0*S0
S=sympy.Matrix([[S1],[S2],[S3]])


    

In [10]:

    

m,th,ph,kx,ky=sympy.symbols('m theta phi kx ky',positive=True)
t,t1,t2,t3,mz=sympy.symbols('t t1 t2 t3 mz',positive=True)


    

In [11]:

    

a1=sympy.Matrix([[sqrt(3)],
           [1]])/2
a2=sympy.Matrix([[-sqrt(3)],
           [1]])/2
k=sympy.Matrix([[kx,ky]])


    

In [12]:

    

U=mataf([[N,N,N,N,t*S0,t*S0],
         [N,N,N,t*S0,t*S0,N],
         [N,N,N,t*S0,N,t*S0],
         [N,t*S0,t*S0,N,N,N],
         [t*S0,t*S0,N,N,N,N],
         [t*S0,N,t*S0,N,N,N]])
T1=mataf([[N,N,N,N,N,N],
          [N,N,N,N,N,t*S0],
          [N,N,N,N,N,N],
          [N,N,N,N,N,N],
          [N,N,N,N,N,N],
          [N,N,N,N,N,N]])
T2=mataf([[N,N,N,t*S0,N,N],
          [N,N,N,N,N,N],
          [N,N,N,N,N,N],
          [N,N,N,N,N,N],
          [N,N,N,N,N,N],
          [N,N,N,N,N,N]])
T3=mataf([[N,N,N,N,N,N],
          [N,N,N,N,N,N],
          [N,N,N,N,N,N],
          [N,N,N,N,N,N],
          [N,N,t*S0,N,N,N],
          [N,N,N,N,N,N]])


    

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