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Aiming at a better understanding of anomalous and topological effects ingauge theories out-of-equilibrium, we study the real-time dynamics of aprototype model for CP-violation, the massive Schwinger model with a$\theta$-term. We identify dynamical quantum phase transitions betweendifferent topological sectors that appear after sufficiently strong quenches ofthe $\theta$-parameter. Moreover, we establish a general dynamical topologicalorder parameter, which can be accessed through fermion two-point correlatorsand, importantly, which can be applied for interacting theories. Enabled bythis result, we show that the topological transitions persist beyond theweak-coupling regime. Finally, these effects can be observed with table-topexperiments based on existing cold-atom, superconducting-qubit, and trapped-iontechnology. Our work, thus, presents a significant step towards quantumsimulating topological and anomalous real-time phenomena relevant to nuclearand high-energy physics.

Dynamical topological transitions in the massive Schwinger model with a {\theta}-term