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There is a well-known mapping between energy normal (super-) diffusion andnormal (anomalous) heat conduction in one-dimensional (1D) nonlinear lattices.The momentum conserving nonlinear lattices exhibit energy super-diffusionbehavior with the only exception of coupled rotator model. Yet, for all other1D momentum nonconserving nonlinear lattices studied so far, the energydiffusion or heat conduction is normal. Here we propose a 1D nonlinear latticemodel with negative couplings, which is momentum non-conserving due to thetranslational symmetry breaking. Our numerical results show that energysuper-diffusion instead of normal diffusion can be found for this model, whichindicates that neither momentum non-conservation is a sufficient condition forenergy normal diffusion nor momentum conservation is a necessary condition forenergy super-diffusion. Zero frequency phonon mode at Brillouin zone boundaryinduces a new conserved momentum parity, which is the key for the energysuper-diffusion and anomalous heat conduction. Removing the zero frequencymode, such as by on-site potential, is a sufficient condition for normal heatconduction in 1D nonlinear lattices.

Energy Super-Diffusion in One-Dimensional Momentum Non-Conserving Nonlinear Lattices