Chaos;head - Blue Complex summary:

Takumi is a high school student. He is withdrawn and is not interested in 3D things. In his town, a mysterious serial murder case happens and people get panicked. One day, when he chats on the internet, a man suddenly contacts him and gives him an URL. He goes to the website and finds a blog image that suggests a next murder case... On the next day, it really happens...Takumi Nishijo suffers from intense delusions as a result of his apparent schizophrenia and the extremely secluded lifestyle he lives as a hikkikomori. One day he accidentally stumbles upon a gruesome murder scene, a part of a chain of events called "New Generation." After this, his life gets caught up in these events, and he meets a bunch of increasingly insane anime girls with swords.