Libertarian Socialism cannot exist simply because the very term itself is contradictory. Broadly simplified, they are infact opposites and saying "Libertarian Socialism" is just like saying "Communistic Capitalism" or "Conservative Progressivism". It is an impossibility. Libertarianism is pretty much only a theory about violence and when it is legitimised or not. In accordance with the NAP then, violence is only justified in terms of self-defense and definied as initiating force to get what you want. A Socialist society is upheld by (i)a central power and (ii)taxes, both of which fall under NAP's definition of violence. However, in a truly Libertarian society, a parallel, Socialist society could exist too. Here the only difference would be that the participation in it would be entirely voluntary- The people who wish to engage in Socialism are free to do so as long everyone else is left alone. This still wouldn't be "Libertarian Socialism" though, but plain, ordinary, simple and classical Socialism.