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

Our Luca Tagliacozzo together with a team of researchers from Jagiellonian University of Cracow, and ICFO uncovers hidden gems lurking behind the Abelian-Higgs model in one spatial dimension and time.
The Higgs mechanism, through which gauge bosons acquire a mass allows to understand how weak interactions can be short-ranged. This mechanism is absent in one spatial dimension due to non-perturbative effects and to the absence of propagating gauge fields. Our recent calculations of the lattice version of the model based on matrix product state however unveil some hidden gems which are the remanent of the 1D Higgs mechanism. They consist in a line of first order phase transitions culminating in a second order phase transition which is exotic.
There the gauge boson emerges as a free particle together with half of the matter field leaving the other half behaving like a free fermion. As a result we observe the emergence of a genuine non-perturbative effect that is better understood through the lenses of entanglement. Our
result thus show how the 1D Abelian Higgs model has been overlooked and it could provide an interesting system where a plethora of exotic features appear. The system thus requires further analysis, whose characterization on the next generation of quantum simulator would provide important insights on the phase diagram and out-of-equilibrium properties of the model.