  A search for events with two displaced vertices from long-lived particles
(LLP) pairs using data collected by the ATLAS detector at the LHC is presented.
This analysis uses 139~fb$^{-1}$ of proton-proton collision data at
$\sqrt{s}=13$ TeV recorded in 2015-2018. The search employs techniques for
reconstructing vertices of LLPs decaying to jets in the muon spectrometer
displaced between 3 m and 14 m with respect to the primary interaction vertex.
The observed numbers of events are consistent with the expected background and
limits for several benchmark signals are determined. For the Higgs boson with a
mass of 125 GeV, the paper reports the first exclusion limits for branching
fractions into neutral long-lived particles below 0.1%, while branching
fractions above 10% are excluded at 95% confidence level for LLP proper
lifetimes ranging from 4 cm to 72.4 m. In addition, the paper present the first
results for the decay of LLPs into into $t\bar{t}$ in the ATLAS muon
spectrometer.
