Quantum centipedes: collective dynamics of interacting quantum walkers

TL;DR

This paper studies the collective dynamics of a quantum centipede composed of interacting fermionic quantum walkers on a 1D lattice, revealing complex ballistic spreading and velocity distribution features due to internal interactions.

Contribution

It introduces an exactly solvable model of interacting quantum walkers, analyzing their spectrum, velocities, and large-N behavior through a mapping to free fermions.

Findings

The quantum centipede exhibits ballistic spreading similar to simple quantum walks.

The velocity distribution shows multiple ballistic fronts with singularities.

Analytical expressions for maximal velocity are derived for arbitrary N.

Abstract

We consider the quantum centipede made of $N$ fermionic quantum walkers on the one-dimensional lattice interacting by means of the simplest of all hard-bound constraints: the distance between two consecutive fermions is either one or two lattice spacings. This composite quantum walker spreads ballistically, just as the simple quantum walk. However, because of the interactions between the internal degrees of freedom, the distribution of its center-of-mass velocity displays numerous ballistic fronts in the long-time limit, corresponding to singularities in the empirical velocity distribution. The spectrum of the centipede and the corresponding group velocities are analyzed by direct means for the first few values of $N$. Some analytical results are obtained for arbitrary $N$ by exploiting an exact mapping of the problem onto a free-fermion system. We thus derive the maximal velocity describing the ballistic spreading of the two extremal fronts of the centipede wavefunction, including its non-trivial value in the large-$N$ limit.