Confinement and Kink Entanglement Asymmetry on a Quantum Ising Chain

TL;DR

This paper investigates how confinement influences entanglement and kink asymmetry in a quantum Ising chain, revealing that confinement can both suppress and enhance entanglement depending on the context.

Contribution

It introduces a numerical approach using tensor networks to analyze entanglement asymmetry in a confined quantum Ising model, including the effects of a longitudinal field.

Findings

Confinement can increase entanglement beyond free particle bounds.

Entanglement asymmetry depends on the treatment of link variables.

Numerical tensor network methods effectively capture entanglement dynamics.

Abstract

In this work, we explore the interplay of confinement, string breaking and entanglement asymmetry on a 1D quantum Ising chain. We consider the evolution of an initial domain wall and show that, surprisingly, while the introduction of confinement through a longitudinal field typically suppresses entanglement, it can also serve to increase it beyond a bound set for free particles. Our model can be tuned to conserve the number of domain walls, which gives an opportunity to explore entanglement asymmetry associated with link variables. We study two approaches to deal with the non-locality of the link variables, either directly or following a Kramers-Wannier transformation that maps bond variables (kinks) to site variables (spins). We develop a numerical procedure for computing the asymmetry using tensor network methods and use it to demonstrate the different types of entanglement and entanglement asymmetry.