Diagonalisation of the Floquet Hamiltonian

The diagonalisation of the matrix representation of Tip can formally be represented by the transformation 

The matrix Ap is diagonal in spin space and in Fourier space, and the block matrix elements of Dp are 

as a result of the diagonalisation, we get a diagonal spin-Hamiltonian 00 and 

Using these definitions we can write the propagator of our spin system in Hilbert space, using Eq. 35, as 

This expression has the same form as Eq. 24, when we define 

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