Quantum entanglement in soliton fractionalisation process

TL;DR

This paper explores quantum entanglement phenomena in relativistic systems involving soliton fractionalisation, linking it to spontaneous symmetry breaking and its implications in condensed matter physics.

Contribution

It introduces a novel perspective on quantum entanglement in relativistic fermion-scalar systems and connects it to spontaneous symmetry breaking phenomena.

Findings

Entanglement occurs between fermion and scalar fields via Yukawa interaction.

Spontaneous symmetry breaking leads to pure state zero-energy solutions.

Relativistic entanglement offers insights into condensed matter symmetry breaking.

Abstract

Quantum state, in relativistic quantum mechanics, itself turns out to be an entangled state due to its own degrees freedom such as spin and momentum. This peculiar entanglement leaves the transformed state mixed. We consider the fractional charge state that arises in a theory of fermion interacting with scalar background in this context. The apparent entanglement occurs between fermion ans scalar through Yukawa-type interaction. However, the spontaneous symmetry breaking causes appearance of the $c$-number zero energy solution of the Dirac equation as a pure state. Quantum entanglement in such relativistic system is proposed to have a microscopic view of the spontaneous symmetry breaking which has been realised in condensed matter system like polyacetylene.