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A constructive algorithm for the Cartan decomposition of SU(2^N)

Henrique N. Sá Earp·Jiannis K. Pachos
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Abstract

We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser decomposition of a general element G of SU(2^N) in terms of its `Cartan' and `non-Cartan' components. This effectively factors G in terms of group elements that belong in SU(2^n) with n<N, a procedure that can be iterated down to n=2. We show that every step reduces to solving the zeros of a matrix polynomial, obtained by truncation of the Baker-Campbell-Hausdorff formula, numerically. All computational tasks involved are straightforward and the overall truncation errors are well under control.

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Henrique N. Sá Earp, Jiannis K. Pachos. 2005-08-16. A constructive algorithm for the Cartan decomposition of SU(2^N). https://doi.org/10.1063/1.2008210

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