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We study a discrete Schr\"odinger equation with arbitrary long range hoppingterms under the influence of an external force. The impact of long rangehoppings on the single particle Bloch dynamics in the lattice is investigated.A closed expression for the propagator is given, based on which we analyze thedynamics of initially Gaussian wave packets. Our findings capture theanharmonic oscillations recently observed in zigzag lattices and furthermoreprovide a detailed quantitative description of the crossover between center ofmass Bloch oscillations for wide wave packets and left-right symmetric widthoscillations for narrow single site excitations. The analytical results areshown to be in agreement with numerical simulations. A helix lattice setup forultracold atoms is proposed where such hopping terms to far neighbors can beexperimentally tuned to sizable values.

Bloch dynamics in lattices with long range hoppings