Gout weed (aegopodium) seems to fit the bill. I had some growing in a box of beach sand, in a closet with the door closed without water. Had I not burned it, it would have broken the door down. However, when it invades your whole neighborhood and the peasants march to your front door carrying torches and pitchforks, don't come crying to me. I warned you.
Some ferns would fit the bill without incurring the wrath of your neighbors, such as Marginal Wood Fern - Dryopteris marginalis, Christmas Fern - Polystichum acrostichoides,and Sensitive Fern - Onoclea sensibilis.
Sensitive fern has grown very well for me and I believe its said to not need 'as much' moisture as many ferns. Sensitive fern will solidly cover an area with fronds up to a foot (or so depending on moisture I think)
That doesn't look like a 'very' wide area. I see your Columbine. I would stick with Columbine and ferns, and tell yourself that some bare ground is OK in midsummer (if it happens) because it is not worth fighting the pine tee roots when you can have ferns and spring flowers.
I'm no fern expert, but I think that is not Sensitive Fern, but rather (maybe) Hay-Scented Fern (http://davesgarden.com/guides/pf/go/52951/). Sensitive Fern has a very unique look, must softer and more delicate than typical ferns.