Calling All Creative Minds....

Gem
Gem, I don't know if you live in "earthquake country." Even if you don't, I have concerns about "wedging a particle board and wood wall between the floor and ceiling." How will it be stabilized? Adding a door to such an unstable wall might be very dangerous. If you decide to proceed with this method, I urge you to place a heavy tall piece of furniture against that wall and screw the wall into the back of the furniture to give it stability.

Instead, you could attach a 2 x 4 board to the ceiling with screws in at least four places in the ceiling wood framing studs, which could be removed and patched and paint touch up when you move. Then you could install a vertical blind hanging from the 2 x 4, which could be closed for privacy and slide open to allow you to enter the room. This would be the most inexpensive project. Or you could install one or two folding doors from the ceiling 2 x 4, which would look better and provide better privacy. It would cost more, but would be worth it.

Either of these two alternatives would be better and safer than a "wedged" wall that could be dangerous and could also damage the apartment wall each time the door is used due to wobble stress on the wall. You may find that they don't cost that much more than the material you would have to buy for the wall and door.

BumbleBeeBoogie

I posted two times already and erased it. I'd just rather suggest a line of tall book shelves and a curtain rod attached between them and a stud in the real wall. Everything else I came up with could conceivably be jerked around if not bolted to floor, ceiling, wall studs and joists, depending on who is living in the room. Even then the bookshelves are susceptible to toppling if not secured to a wall.. in earthquake country or with rambunctious folk.

I suppose you could add "barn doors" on a ceiling track, again, attached via ceiling joists, which, really, I would ask your landlord first. The barn doors, so called, could be lightweight, some sort of hollow core items you rig up yourself and attach to track apparatus.

I would use a bifold door. Or two of them depending on the size you need. They're light and don't need a strong pivot point like the hinges on a door.

BBB
Gem, What we are all saying is that a wedged wall and door is not safe for the use you describe.

BBB