Student or Learner
According to LDCE:
allotment: BrE a small area of land that people
can rent for growing vegetables
I wonder what is the American equivalent.
I don't know of any place in the U.S. where you'd rent land just to grow vegetables. Often if you rent a home, there is a back yard (what Brits call a "garden") that comes with it, and you're welcome to plant whatever you want there. By the way, in AmE, a "garden" is strictly an area of land where flowers or vegetables are grown. The grassy area in front and in back of the house is the "yard."
Thank you very much, everybody.
Incidentally, you may have got the impression that allotments are just for growing vegetables; they are used here for growing anything: vegetables, fruit, and flowers.