Entanglement of Solitons in the Frenkel-Kontorova Model

TL;DR

This paper explores how solitons in the Frenkel-Kontorova model exhibit particle-like entanglement properties, revealing complex behaviors including localization, mixed criticality, and long-range entanglement, with implications for quantum information.

Contribution

It provides a detailed analysis of soliton entanglement in the continuum limit, highlighting localization, mixed criticality, and long-range effects, and proposes using internal modes for quantum information transfer.

Findings

Entanglement of solitons shows particle-like localization.

Logarithmic entropy increase is faster inside the soliton core.

Long-range entanglement decreases slowly with separation, even increasing in noncritical regimes.

Abstract

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.