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

We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser decomposition of a general element G∊SU(2N) in terms of its “Cartan” and “non-Cartan” components. This effectively factors G in terms of group elements that belong in SU(2n) 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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