  Results of a search for new physics in final states with an energetic jet and
large missing transverse momentum are reported. The search uses proton-proton
collision data corresponding to an integrated luminosity of 139 fb$^{-1}$ at a
center-of-mass energy of 13 TeV collected in the period 2015-2018 with the
ATLAS detector at the Large Hadron Collider. Compared to previous publications,
in addition to an increase of almost a factor of four in the data size, the
analysis implements a number of improvements in the signal selection and the
background determination leading to enhanced sensitivity. Events are required
to have at least one jet with transverse momentum above 150 GeV and no
reconstructed leptons ($e$, $\mu$ or $\tau$) or photons. Several signal regions
are considered with increasing requirements on the missing transverse momentum
starting at 200 GeV. Overall agreement is observed between the number of events
in data and the Standard Model predictions. Model-independent 95 %
confidence-level limits on visible cross sections for new processes are
obtained in the range between 736 fb and 0.3 fb with increasing missing
transverse momentum. Results are also translated into improved exclusion limits
in models with pair-produced weakly interacting dark-matter candidates, large
extra spatial dimensions, supersymmetric particles in several compressed
scenarios, axion-like particles, and new scalar particles in
dark-energy-inspired models. In addition, the data are translated into bounds
on the invisible branching ratio of the Higgs boson.
