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We consider the quantum centipede made of $N$ fermionic quantum walkers onthe one-dimensional lattice interacting by means of the simplest of allhard-bound constraints: the distance between two consecutive fermions is eitherone or two lattice spacings. This composite quantum walker spreadsballistically, just as the simple quantum walk. However, because of theinteractions between the internal degrees of freedom, the distribution of itscenter-of-mass velocity displays numerous ballistic fronts in the long-timelimit, corresponding to singularities in the empirical velocity distribution.The spectrum of the centipede and the corresponding group velocities areanalyzed by direct means for the first few values of $N$. Some analyticalresults are obtained for arbitrary $N$ by exploiting an exact mapping of theproblem onto a free-fermion system. We thus derive the maximal velocitydescribing the ballistic spreading of the two extremal fronts of the centipedewavefunction, including its non-trivial value in the large-$N$ limit.

Quantum centipedes: collective dynamics of interacting quantum walkers