You can try covering the area and a bit outside the surrounding area with clear plastic sealed to the ground with boards or rocks around the edges. It will get so hot under there (greenhouse effect) that it will overheat the plants basically steaming them to death. This method works best when it is very hot and sunny outside already. It is important that the plastic be sealed to the ground all the way around to trap all the heat.
If this fails (it usually doesn’t if it is hot and sunny enough) then you’ll have to resort to a soil sterilizing chemical like Bonide total. This is a soil drench and will kill any plant it comes in contact with the roots of. It needs to be used with EXTREME caution since it can leach into the soil and kill desirable plants, shrubs and tree nearby.