Q.Mugwort Control: Tips For Getting Rid Of Mugwort
The above article was written by Bonnie Grant and mentions simply placing a tarp over the Mugwort if you have an area that will undergo complete rejuvenation. My question is, for how many months should the tarp be left down to ensure that the Mugwort rhizomes are depleted and dead?

Certified GKH Gardening Expert
Solarization should kill the weed roots but may not be enough to kill bulbs, rhizomes, etc.
Chemical control is doable, but even that will take two years. If you want to try the tarp method first, leave it down for two to three months. In winter, leave it for six months. Here is more from university extension:
https://ucanr.edu/blogs/blogcore/postdetail.cfm?postnum=6980