I see (and like!) the accepted answer, but here's what I came up with that I think is also pretty reasonable:
Sub-atomic matter, particularly in the context of the atomic bomb.
In the darkness, I stay hidden,
These particles are extremely hard to detect, plus you have the whole quantum debacle
then with the cleansing sweep,
The detonation of an atomic bomb.
I step out from the shadows, as I watch the whole world weep.
The weaponizing of an atomic bomb is very visible, but also extremely tragic if used to take lives.
I was torn apart, my body bent, forever segregated.
The atom as a whole is torn apart. Not sure about the bent part. The weaponizing of atomic bombs in WW2 creates a 'permanent segregation' of sorts -- there are 'prewar' and 'postwar' eras.
Broken, I at first give life. Then as a weapon, take it.
Big bang, etc., vs. weaponization of atomic energy.
Elusive, you won't trap me, nor the hoard kept at my feet,
We can't ever know the position and velocity of a sub-atomic particle simultaneously, so they're elusive and 'untrappable'. The hoard at its feet could be those new-fangled particles like gluons and such.
Sometimes haunted by my twin, though cursed to never meet.
Riding on your gallows, bathed in violence, I start.
Again, bomb stuff
Say my name, mere mortal, before I again depart.
As more regulations and treaties are signed, the chances of future nuclear war diminishes.