  Xenon dual-phase time projection chambers designed to search for Weakly
Interacting Massive Particles have so far shown a relative energy resolution
which degrades with energy above $\sim$200 keV due to the saturation effects.
This has limited their sensitivity in the search for rare events like the
neutrinoless double-beta decay of $^{136}$Xe at its $Q$-value,
$Q_{\beta\beta}\simeq$ 2.46 MeV. For the XENON1T dual-phase time projection
chamber, we demonstrate that the relative energy resolution at 1 $\sigma/\mu$
is as low as (0.80$\pm$0.02) % in its one-ton fiducial mass, and for
single-site interactions at $Q_{\beta\beta}$. We also present a new signal
correction method to rectify the saturation effects of the signal readout
system, resulting in more accurate position reconstruction and indirectly
improving the energy resolution. The very good result achieved in XENON1T opens
up new windows for the xenon dual-phase dark matter detectors to simultaneously
search for other rare events.
