  A novel search for exotic decays of the Higgs boson into pairs of long-lived
neutral particles, each decaying into a bottom quark pair, is performed using
139 fb$^{-1}$ of $\sqrt{s} = 13$ TeV proton-proton collision data collected
with the ATLAS detector at the LHC. Events consistent with the production of a
Higgs boson in association with a leptonically decaying $Z$ boson are analysed.
Long-lived particle (LLP) decays are reconstructed from inner-detector tracks
as displaced vertices with high mass and track multiplicity relative to
Standard Model processes. The analysis selection requires the presence of at
least two displaced vertices, effectively suppressing Standard Model
backgrounds. The residual background contribution is estimated using a
data-driven technique. No excess over Standard Model predictions is observed,
and upper limits are set on the branching ratio of the Higgs boson to LLPs.
Branching ratios above 10% are excluded at 95% confidence level for LLP mean
proper lifetimes $c\tau$ as small as 4 mm and as large as 100 mm. For LLP
masses below 40 GeV, these results represent the most stringent constraint in
this lifetime regime.
