Entanglement in One-Dimensional Spin Systems

TL;DR

This paper investigates how entanglement propagates and transforms in one-dimensional anisotropic XY spin systems, revealing velocity-dependent propagation, state transmutation, and localized entanglement waves.

Contribution

It provides a detailed analysis of entanglement dynamics, including propagation velocity, state transmutation, and creation from polarized states in anisotropic XY models.

Findings

Entanglement propagates with velocity proportional to reduced interaction.

A transmutation from singlet-like to triplet-like states occurs during propagation.

Entanglement creation from a fully polarized state is instantaneous and localized.

Abstract

For the anisotropic XY model in transverse magnetic field, we analyze the ground state and its concurrence-free point for generic anisotropy, and the time evolution of initial Bell states created in a fully polarized background and on the ground state. We find that the pairwise entanglement propagates with a velocity proportional to the reduced interaction for all the four Bell states. A transmutation from singlet-like to triplet-like states is observed during the propagation. Characteristic for the anisotropic models is the instantaneous creation of pairwise entanglement from a fully polarized state; furthermore, the propagation of pairwise entanglement is suppressed in favor of a creation of different types of entanglement. The ``entanglement wave'' evolving from a Bell state on the ground state turns out to be very localized in space-time. Our findings agree with a recently formulated conjecture on entanglement sharing; some results are interpreted in terms of this conjecture.