Finding the eigenvalues (diagonalizing) of a block-diagonal matrix

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Finding the eigenvalues (diagonalizing) of a block-diagonal matrix

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I have to diagonalize a large matrix which take a lot of time. The matrix size 10,000 x 10,000.

This matrix is Hamiltonian of a spin system which have some block structure. Is there way to diagonalize the full matrix by diagonalize each block ?

Basically I want to

1. permutate the matrix to reduce to a block structure

2. Diagonalize each blocks .

I would appreciate any help.

Thanks.

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