batsbrew
and they are designed SPECIFICALLY for sound absorbtion, not for moving furniture.
and they are WAY more efficient than foam.
i know, i've tried both.
Sorta kinda, and sadly the web page for the product is the source of the confusion! I really wish vendors in this space would try to be more accurate!
The blanets that Bat is suggesting will provide isolation, or transmission loss, between adjoining spaces - and that's what they are designed to do. They probably won't provide a lot of absorption, except at very high frequencies, and absorption is not even specified... which makes sense.
There is a lot of confusion surrounding room treatment. The short version:
Room treatments can be divided into two basic categories - soundproofing (isolation or transmission loss) and room behavior, which includes absorption, diffusion, and reflection.
I'm not really clear on what the OP is trying to accomplish, but since Bat brought up those blankets let's tackle isolation first.
The goal is to prevent sound from entering, or leaving, the space. The ONLY solutions are mass (preferably a limp mass) and an airtight space. Since the later is rather impractical<G>, most folks go with mass. Adding mass to the walls won't be practical since the space is rented, but some mass can be added by using loaded vinyl sheets or loaded blankets - which the referenced product appears to be. Note that you need a LOT of mass to stop low frequency energy, but not too much for higher frequencies.
Some of the questions and comments suggest that the OP is looking to simply treat the room to make it more listenable.
This may not be as difficult as it first appears. Since the room is small it is not reverberant, which means that only the 'bad' reflections need to be treated. The size also limits the room modes that can build up, meaning there should be few low frequency bumps.
If room treatment is the goal I would suggest getting a lot more info on the blankets, since they will not absorb much (according to the published specifications anyway.) But if isolation is the goal they look like a great starting point!