Spectral properties of the critical (1+1)-dimensional Abelian-Higgs model

The presence of gauge symmetry in 1+1 dimensions is known to be redundant, since it does not imply the existence of dynamical gauge bosons. As a consequence, in the continuum, the Abelian-Higgs model (i.e., the theory of bosonic matter interacting with photons) just possesses a single phase, as the higher-dimensional Higgs and Coulomb phases are connected via nonperturbative effects. However, recent research published in Phys. Rev. Lett. 128, 090601 (2022), 10.1103/PhysRevLett.128.090601 has revealed an unexpected phase transition when the system is discretized on the lattice. This transition is described by a conformal field theory with a central charge of c =3 /2 . In this paper, we aim to characterize the two components of this c =3 /2 theory—namely the free Majorana fermionic and bosonic parts—through equilibrium and out-of-equilibrium spectral analyses.