In short, if it's a rented apartment where you can't make permamnent changes, then you are somewhat stuffed in terms of soundproofing. To reduce sound transmission by any appreciable amount, you need mass, and lots of it. You would at least need to be looking at a room-within-a-room type construction.
For acoustic treatment, then there's much more you can do with free-standing and wall hanging broadband absorbers and bass traps.
You should start off by reading the sticky threads in this very section of the forum as well as Trev's informative post on the subject:
Treating a domestic sized room