There are certainly examples where some polymers can leach solvents or plasticizers or whatever. But, having studied a little polymer chemistry, I personally am not concerned with what you are doing.
I have no specific scientific basis for making that judgement about your particular polymer, except that it was designed to be pretty stable in the presence of sunlight and
water.
I think it is unfair to label all plastics as evil and dangerous because they leach. Look at it from the other side of the coin for a minute. One of the problems with most polymers is that they are so danged persistent in the environment. So I have a little problem with folks who claim on the one hand that plastics are evil because they're not biodegradable and hang around for centuries, and on the other hand, that claim they are leaching all kinds of toxic chemicals into the soil and the groundwater. You really can't have it both ways.
Further, in healthy soil, there are jillions of bacteria, fungi, protozoa, invertebrates, and on and on and tens of thousands of different species. It turns out that there are not too many things they can't eat, or surround and neutralize (bio-remediation).
So, I don't go dumping weird chemicals on my soil willy nilly, but I don't lose sleep over whatever minute amount of stuff might be leaching out of your plastic.
Would I be happier with a polymer made from corn starch that biodegraded quickly after 3 years? Maybe. And maybe/probably it came from evil GMO FrankenCorn that's screwing up the countryside rapidly, so maybe not.
Certainly, your plastic sheeting that is under mulch/soil will break down chemically very very slowly, and by extension, leach stuff into your soil very very slowly. Probably insignificantly.
That's my educated gut feeling.
Degree in chemistry and biology, and organic gardener for 30 years, for whatever those qualifications are worth.
Oh yeah, and I'm a doctor and have some formal training in toxicology.
I would bet my last pair of socks that your food from your land, even though it touched a piece of plastic, is better than the food at 99% of the grocery stores in terms of chemical residue.
HTH,
troy