  Materials with tunable charge and lattice degrees of freedom provide
excellent platforms for investigating multiple phases that can be controlled
via external stimuli. We show how the charge-ordered ferroelectric oxide
Ag$_2$BiO$_3$, which has been realized experimentally, presents a unique
exemplar of a metal-insulator transition under an external electric field. Our
first-principles calculations, combined with a symmetry analysis, reveal the
presence of a nearly ideal hourglass-Dirac-semimetal state in the nonpolar
structure of Ag$_2$BiO$_3$. The low-energy band structure consists of two
hourglasslike nodal lines located on two mutually orthogonal glide-mirror
planes in the absence of spin-orbit coupling (SOC) effects. These lines cross
at a common point and form an interlinked chainlike structure, which extends
beyond the first Brillouin zone. Inclusion of the SOC opens a small gap in the
nodal lines and results in two symmetry-enforced hourglasslike Dirac points on
the $\tilde{\mathcal{C}}_{2y}$ screw rotation axis. Our results indicate that
Ag$_2$BiO$_3$ will provide an ideal platform for exploring the
ferroelectric-semiconductor to Dirac-semimetal transition by the application of
an external electric field.
