Tee: Disregard my post ... looking closer the plant in question doesn't appear to be Persicaria. Your plant sure looks familiar ... I swear I had the same stuff or something very similar sprouting up in the lawn at my old house. I thought I had it ID'd but can't for the life of me remember the name. I've gone through all my photo's in my "weed" folder and can't find it.
It may have been in my plant photo's that I lost when my laptop crashed a year or so ago.
Hopefully someone will come along and recognize it but I will continue to rack my brain and try to remember the one I had ... may not even be close but it sure looks like it and I remember the new shoots being kind of stiff, not soft at all. I used to mow it down so I never saw any blooms.