How do you get rid of nut grass in the garden?
Most perennials are extremely susceptible to tillage. The key is to stay with it—do it several times in a season. As you expose the roots to the top of the soil, they will either freeze or bake in the sun. Whenever I have a perennial infestation, I make sure I plant something that will require soil disturbance mid-season—like sweet corn or potatoes, which will be hilled after they are up a bit. This mid-season disturbance puts the perennials on the run.
Of course, double-cropping or even triple-cropping can be a great help. Early radishes or beets followed by tomatoes, peppers, or squash, then a late planting of Swiss chard or spinach will give you several tillage opportunities. And when I say tillage, I’m not requiring a garden tiller. It can be a spade, broad fork, or shovel even. The point is to disturb the soil down at least six inches to keep the perennial from acquiring energy equilibrium (the point where photosynthetic activity has replaced the energy in the roots that was expended in sending forth the shoots).