Cutting alone will not eliminate weeds. Using a tarp for a year seems excessive and will be unsightly. Solarizing with plastic also destroys beneficial soil organisms.

Instead of a tarp, you can Round Up everything remaining, wait 2 weeks, Round Up anything that is still green and repeat until all is dead. Wait a week or two for the first Round Up application as you need enough green leaves on the plants for Round Up to work. For severe thistles, repeated applications of Round Up is the best control. Once everything is dead, cover the yard with 3-4 inches of mulch to prevent weed seeds from taking hold.

You will still need to pull any weeds that show up but they will be small and easy to pull from the mulch. Perennials could be planted now (will need watering) or in the fall.

For chemical free control, you can cover all with 5-6 layers of moist newspaper, then cover with 3-4 inches of mulch. You can plant into this after 6-8 weeks, but may find the thistles survive it.

Although I have not tried it, I read about a method in Linda Tilgner's 'Tips for the Lazy Gardener'. She says to plant at least 3 consecutive crops of buckwheat, making sure the cut it down before it goes to seed. She says that it will crowd most weeds out, and if you leave it in place when you cut it down, it will rot & amend the soil.

I have a large weed patch that used to be a vegetable garden, but in the last years, the former owners let go to weeds (they were pretty old & frail in the end), and I was thinking about trying it as I'd like to get a veggie garden going myself.

Later,
Gail

Planting buckwheat might work on bare soil to prevent weed seeds from taking hold, but it won't prevent the cut trees, thistles etc from coming back. They will need to be killed.