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I am new to the Tensor network approach. I need to solve the eigenvalue problem for a Matrix product Operator (MPO). What are some techniques, resources, softwares or packages available to do it? I am specifically interested in eigenvalues with value equal to 1, and the corresponding eigenvector (all eigenvalues have absolute values less than or equal to one). Any guidance will be very helpful. Thanks.

Edit: I just found out that power iteration method to solve the eigenvalue problem might work. Are there other/numerically more efficient methods?

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I know that using Tensor network approach, one can efficiently act a MPO on a Matrix product state (MPS) to get an output MPS. This is because although MPO can be seen a large matrix that acts on vector (that is, the MPS), after using Singular value decomposition (SVD), we will be effectively dealing with a matrix of much smaller dimensions.

My question is, when MPO acts on a MPS, one gets a MPS that may not be the scaled version of the input MPS. So, how does one go about solving the eigenvalue problem from here?

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A great resource is J. Haegeman and F. Verstraete, Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods

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