The Schwinger model : spectrum, dynamics and quantum quenches (2018)
Quantum electrodynamics in two dimensions (one spatial dimension + time) with Dirac fermions was a model first studied by Julian Schwinger in 1962 and thus it was coined the Schwinger model. The massless model is completely solvable and shows very interesting physical phenomena such as a chiral anomaly, a massive boson generated via a kind of dynamical Higgs mechanism, the presence of confinement analogous to quark confinement in QCD 4 and spontaneous symmetry breaking of a U(1) axial symmetry. The Schwinger model is the simplest gauge theory being completely solvable, thus, it is a rich toy model for studying more complex gauge theories. In this work, we quantize the Schwinger model using Hamiltonian quantization in the temporal Weyl gauge (A0 = 0) which then can be written as a lattice system of spins using Kogut-Susskind fermions and a Jordan-Wigner transformation. This lattice model is numerically studied using exact diagonalization methods. We study the ground state energy, the first few excited states energies, the existence of a gap and the order parameter values both in the free massless and massive model. Additionally, we explore the dynamical evolution of the spectrum of the Dirac operator, the dynamics of the ground state and the behavior of order parameters such as the chiral condensate density as a consequence of the introduction of global quenches in the system in both the massless and the massive interacting models in the presence of a background electric field.