Efficient linear scaling mapping for permutation symmetric Fock spaces

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Numerically solving a second quantised many-body model in the permutation symmetric Fock space can be challenging for two reasons: (i) an increased complication in the calculations of the matrix elements of various operators, and (ii) a poor scaling of the cost of these calculations with the Fock space size. We present a method that solves both these problems. We find a mapping that can be used to simplify the calculations of the matrix elements. The mapping is directly generated so its computational cost scales only linearly with the space size and is negligible even for large enough sizes that approach the thermodynamic limit. A fortran implementation of the method as a library – FockMap – is provided along with a test program.

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