Phase Diagram of 1+1D Abelian-Higgs Model and Its Critical Point

We determine the phase diagram of the Abelian-Higgs model in one spatial dimension and time ($1+1\mathrm{D}$) on a lattice. We identify a line of first order phase transitions separating the Higgs region from the confined one. This line terminates in a quantum critical point above which the two regions are connected by a smooth crossover. We analyze the critical point and find compelling evidence for its description as the product of two noninteracting systems: a massless free fermion and a massless free boson. However, we find also some surprising results that cannot be explained by our simple picture, suggesting this newly discovered critical point is an unusual one.