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Frequent observation of a quantum system leads to quantum Zeno physics, wherethe system evolution is constrained to states commensurate with the measurementoutcome. We show that, more generally, the system can evolve between suchstates through higher-order virtual processes that pass through states outsidethe measurement subspace. We derive effective Hamiltonians to describe thisevolution, and the dependence on the time between measurements. We demonstrateapplication of this phenomena to prototypical quantum many-body systemexamples, spin chains and atoms in optical lattices, where it facilitatescorrelated dynamical effects.

Quantum Quasi-Zeno Dynamics: Transitions mediated by frequent projective measurements near the Zeno regime