When I lived in an apartment I had the same problem so I got some blue hard foam insulation (it was 2 inches thick and 4x8 ft sheets)and made a wall. I covered both sides with quilting material and then covered the side facing into the room with a very dense material from the cheap bin at the local fabric store. The new wall fit snuggly in place with about a two inch air pocket between it and the original wall. It held in place because I made sure the side walls and ceiling made a snug fit. It blocked out most of the sound going through that wall. Another thing I did was decouple the speakers from the floor using cork material plus a hockey puck as feet under the speakers. I was able to crank up the volume and never had a complaint in the two years I lived there. It was relitively cheap on the front end and the new tenent liked it so much she paid me exactly what it cost me.
It takes a little time to measure it and put everthing together but remember it's all for the joy of listening and enjoying the music.
