Libertarianism is a theory of law: it explains that conflicts between humans are minimized when they recognize each other's property rights, based on self-ownership and homesteading of unowned resources, preserved by transformation through labor, and transmitted through consensual trading and giving.
Um, no. Libertarianism isn't a theory, of law or of anything else.
Libertarianism is a constraint -- the non-aggression principle.
There are any number of philosophical foundations from which one may build up to the discovery of this constraint. No, I'm not saying all of those foundations are valid. I'm just saying that there are many roads leading to Rome. Some may be straight and smoothly surfaced, some may be winding and full of potholes. And that's important. But for our purposes here, how you get here not as important as where here is and what's on this spot. Libertarianism is the non-aggression principle, not the things leading to the non-aggression principle.
Any number of theories of social and political organization might be reasoned out, visualized or implemented which adhere to this constraint. A theory which adheres to this constraint is libertarian in character (but is not libertarianism itself). A theory which does not adhere to this constraint is "libertarian" neither in character nor in any other sense. Libertarianism is the non-aggression principle, not every conclusion which might be (correctly or incorrectly) derived from the non-aggression principle.
"Left" and "right" and "thin" and "thick" and so forth are prospectively valid additive adjectives for describing these theories and the people who adhere to them.
And while I'm speaking ex cathedra anyway, I'll go ahead and posit that "left-libertarian" is a redundancy, that "right-libertarian" and "vulgar libertarian" are synonyms for "libertarians in error" and that "anarcho-capitalist" is an oxymoron.