A dynamical Lie algebraic method for the construction of quantum invariants of motion in non-integrable many-body systems of infinite size is proposed and applied to a simple but generic toy model, namely an infinite kicked t - V chain of interacting spinless fermions. The transition from an integrable via quasi-integrable ( intermediate) to a quantum ergodic (quantum mixing) regime in parameter space is investigated. A dynamical phase transition between an ergodic and intermediate (neither ergodic nor completely integrable) regime in thermodynamic limit is proposed. The existence or non-existence of local conservation laws corresponds to the intermediate or ergodic regime, respectively. The computation of time-correlation functions of typical observables by means of local conservation laws is found to be fully consistent with direct calculations on finite systems.