  Nuclei around $N\approx Z\approx 40$ are strongly deformed and exhibit
coexistence of shapes. These phenomena have challenged nuclear models. Here we
perform ab initio coupled-cluster computations of low-lying collective states
and electromagnetic quadrupole transitions of the even-even nuclei $^{72}$Kr,
$^{76,78}$Sr, $^{78,80}$Zr and $^{84}$Mo starting from chiral nucleon-nucleon
and three-nucleon forces. Our calculations reproduce the coexistence of oblate
and prolate shapes in these nuclei, yield rotational bands and strong
electromagnetic transitions, but are not accurate for some observables and
nuclei. These results highlight the advances and challenges of ab initio
computations of heavy deformed nuclei.
