Title: Classification of Floquet drives of one-dimensional fermions.

One of the recent developements in condensed matter is the idea that there can exist new phases of matter in periodically driven Floquet systems that are absent in equilibrium. In the presence of global symmetries, it was shown by von Keyserlingk et al. that we could have new symmetry-protected-topological (SPT) phases characterized by the existence of robust ‘pumped’ boundary modes that are absent in equilibrium. Roy and Harper provided an alternative perspective on these phases in terms of a classification of loop-unitaries (time evolution operators of the form U(t)| U(0) = U(T) = 1). From this point of view, the Floquet-SPT phases that are unique to the driven setting are those that correspond to loop-unitaries that cannot be deformed to a trivial one (U(t) = 1) without breaking symmetry. In this work, we use Roy and Harper's scheme to study how the classification of driven one dimensional free-fermion phases for the different Altland-Zirnbauer symmetry classes changes in the presence of interactions. We find our results to be in agreement with those obtained by von Keyserlingk et al.