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We use chiral interactions and several {\em ab initio} methods to compute thenuclear matrix elements (NMEs) for ground-state to ground-state doubleGamow-Teller transitions in a range of isotopes, and explore the correlation ofthese NMEs with those for neutrinoless double beta decay produced by theexchange of a light Majorana neutrino. When all the NMEs of bothisospin-conserving and isospin-changing transitions from the {\em ab initio}calculations are considered, the correlation is strong. For the experimentallyrelevant isospin-changing transitions by themselves, however, the correlationis weaker and may not be helpful for reducing the uncertainty in the NMEs forneutrinoless double-beta decay.

Ab initio studies of double Gamow-Teller transition and its correlation with neutrinoless double beta decay