Entanglement of Solitons in the Frenkel-Kontorova Model
  We investigate entanglement of solitons in the continuum-limit of the nonlinear Frenkel-Kontorova chain. We find that the entanglement of solitons manifests particle-like behavior as they are characterized by localization of entanglement. The von-Neumann entropy of solitons mixes critical with noncritical behaviors. Inside the core of the soliton the logarithmic increase of the entropy is faster than the universal increase of a critical field, whereas outside the core the entropy decreases and saturates the constant value of the corresponding massive noncritical field. In addition, two solitons manifest long-range entanglement that decreases with the separation of the solitons more slowly than the universal decrease of the critical field. Interestingly, in the noncritical regime of the Frenkel-Kontorova model, entanglement can even increase with the separation of the solitons. We show that most of the entanglement of the so-called internal modes of the solitons is saturated by local degrees of freedom inside the core, and therefore we suggest using the internal modes as carriers of quantum information. 
Samuel Marcovitch and Benni Reznik