Phase diagram of 1+1D Abelian-Higgs model and its critical point

Abstract

We determine the phase diagram of the Abelian-Higgs model in one spatial dimension and time (1+1D) 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 evidences for its description as the product of two non-interacting systems, a massless free fermion and a massless free boson. However, we find also some surprizing results that cannot be explained by our simple picture, suggesting this newly discovered critical point to be an unusual one.

6+3 pages, 4+6 figures. Version accepted in PRL

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• Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder
• Gapless deconfined phase in a ${\mathbb{Z}}_N$ symmetric Hamiltonian created in a cold-atom setup