  The $2\nu\beta\beta$-decay nuclear matrix elements (NMEs) for 11 nuclei are
studied with the self-consistent quasiparticle random phase approximation
(QRPA) based on Skyrme Hartree-Fock-Bogoliubov (Skyrme HFB) model. As a common
feature pointed out in
https://journals.aps.org/prc/abstract/10.1103/PhysRevC.98.064325 Phys. Rev. C
98, 064325 (2018), negative contributions in the running sums of NMEs are
found, and play important roles in the fulfillment of the single-state
dominance or low-lying-states dominance hypothesis. By comparing the results of
QRPA model and quasiparticle Tamm-Dancoff approximation (QTDA) model, we find
that the negative contributions are due to the enhanced ground-state
correlations, which are brought by the backward amplitude in QRPA model and
tuned by strong isoscalar pairing interaction. The enhancement of ground-state
correlations will change the signs of GT$^{+}$ transition amplitudes of
higher-lying states and leads to the negative contributions in the running sum.
