Yamibo - Darkness, the Hat, and the Travelers of the Books

Hatsuki is a high-school student living with Hatsumi, and the two are so close they are like sisters. On Hatsumi's 16th birthday, she is suddenly surrounded by a green light and disappears right in front of Hatsuki! Hatsuki manages to follow Hatsumi with the help of a yellow parakeet named Ken, and ends up in a place called "The Great Library," full of different worlds stored in books. But Hatsumi isn't there, and so the search begins...