  Suppose a quantum system starts to evolve under a Hamiltonian from some
initial state. When for the first time, will an observable attain a preassigned
value? To answer this question, one method often adopted is to make
instantaneous measurements periodically and note down the serial number for
which the desired result is obtained for the first time. We apply this protocol
to an interacting spin system at zero temperature and show analytically that
the response of this system shows a non-analyticity as a function of the
parameter of the Hamiltonian and the time interval of measurement. In contrast
to quantum phase transitions, this new type of phase transition is not a
property of the ground state and arises from the Hamiltonian dynamics and
quantum mechanical nature of the measurement. The specific system studied is
transverse Ising chain and the measurement performed is, whether the total
transverse magnetic moment (per site) is not equal to 1. The results for some
other types of measurement is also discussed.
