"You're like a millennial Natalie Portman. Like I'm V for Vendetta." (1.17). After Gus says this Hazel goes over and watches V for Vendetta with him. Him telling her this starts off their whole relationship. If he never said anything to her though, they probably would not have ever met or dated.
"Hazel and I are going to watch V for Vendetta so she can see her filmic doppelganger, mid-two thousands Natalie Portman" (2.29). Augustus and Hazel watch V for Vendetta on their first date after support group. Augustus introduces Hazel to his parents and shows her his room after a dinner of enchiladas.
This is a difference from the book and movie. In the book Gus wants to watch V for Vendetta in the basement but his parents make them watch it upstairs in the living room and none of that happens in the movie