Abstract
We study the dynamics of the massive Schwinger model on a lattice using exact diagonalization. When periodic boundary conditions are imposed, analytic arguments indicate that a non-zero electric flux in the initial state can "unwind" and decrease to a minimum value equal to minus its initial value, due to the effects of a pair of charges that repeatedly traverse the spatial circle. Our numerical results support the existence of this flux unwinding phenomenon, both for initial states containing a charged pair inserted by hand, and when the charges are produced by Schwinger pair production. We also study boundary conditions where charges are confined to an interval and flux unwinding cannot occur, and the massless limit, where our results agree with the predictions of the bosonized description of the Schwinger model.
Highlights
The massive Schwinger model [1]—quantum electrodynamics in one space and one time dimension—is a fascinating quantum field theory that has been studied intensively since the 1950s
Despite the absence of electromagnetic waves in one spatial dimension, the electric field in the Schwinger model is generally time-dependent because charged particles move and affect its value. These particles can be spontaneously produced by Schwinger pair production in the quantum theory [7], or be present in the initial state
We study the dynamics of the model with OBC
Summary
The massive Schwinger model [1]—quantum electrodynamics in one space and one time dimension—is a fascinating quantum field theory that has been studied intensively since the 1950s. Despite the absence of electromagnetic waves in one spatial dimension, the electric field in the Schwinger model is generally time-dependent because charged particles move and affect its value. These particles can be spontaneously produced by Schwinger pair production in the quantum theory [7], or be present in the initial state. We study the time-evolution of the zero-electric field ground state and show that Schwinger pair production occurs and leads to flux unwinding. We examine the lattice version of the Schwinger model and study several time-dependent phenomena in a variety of parameter regimes and for several different initial states. Transitions between these states of L that allow for the unwinding mechanism as discussed in [8], which cannot occur for OBC where L is not a d.o.f
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