Date a Live: Another World Volume 1

Spatial Quakes, a destructive supernatural phenomenon that consumes everything in its wake whenever it appeared. To some people, it's a disaster. But to a selected few, Spatial Quakes are a different thing entirely as it signified that a Spirit, an extraterrestrial cosmic entity whose power was able to bend the laws of physics has appeared.

20 years Ago....
Two simultaneous Spatial Quakes caused by a pair of twin spirits, Natsuro and Neri Yamago, hits Tengu City. Fortunately, they managed to escape from the clutches of the Anti-Spirit Team, a military branch whose sole goal was to subdue spirits by eliminating them.
In Present Day, the two of them managed to blend into society and lived normal lives as they hid their true identities as spirits from the world. Unfortunately, it won't last for long as one Spatial Quake during a day at school will change everything.

During the quake, they learnt that they were not the only spirits on Earth and there is a force much more menacing than the Anti Spirit Team.
The Yamago twins must now cooperate with their fellow spirits and an organization known as Ratatoskr, who focused on handling spirits through peaceful means... Only if they didn't want themselves or their fellow spirits be injured or worse... KILLED.