近日，英国伦敦大学的Michele Mazzoni及其研究团队取得一项新进展。经过不懈努力，他们对扭结激发态的纠缠特性进行研究。相关研究成果已于2025年2月6日在国际知名学术期刊《高能物理杂志》上发表。

在本工作中，该研究团队研究了扭结激发态的纠缠熵。首先，研究人员对自旋-1/2链的特定状态进行了详细计算，以突出这些激发态的显著特征。其次，研究人员基于扭结场与与激发态相关的半局域场之间的代数关系，提供了一个场论框架，并在此框架内计算了雷尼熵。

研究人员获得了有限数量扭结激发态与对称性破缺基态之间的熵差的普适性预测，在大区域极限下，这一预测不依赖于模型的具体微观细节。最后，研究人员讨论了克拉默斯-瓦尼尔对偶性的一些后果，该对偶性关联了伊辛模型的有序相和无序相，并解释了为何在纠缠层面上未能直观地发现这些相之间的明确关系。

据悉，在有序相中，一维量子系统的基本激发态为其对称性破缺真空之上的扭结。虽然扭结的散射特性类似于准粒子，但它们在纠缠熵方面表现出独特的局域性特征。

附：英文原文

Title: Entanglement content of kink excitations

Author: Capizzi, Luca, Mazzoni, Michele

Issue&Volume: 2025-02-06

Abstract: Quantum one-dimensional systems in their ordered phase admit kinks as elementary excitations above their symmetry-broken vacua. While the scattering properties of the kinks resemble those of quasiparticles, they have distinct locality features that are manifest in their entanglement content. In this work, we study the entanglement entropy of kink excitations. We first present detailed calculations for specific states of a spin-1/2 chain to highlight the salient features of these excitations. Second, we provide a field-theoretic framework based on the algebraic relations between the twist fields and the semilocal fields associated with the excitations, and we compute the Rényi entropies in this framework. We obtain universal predictions for the entropy difference between the excited states with a finite number of kinks and the symmetry-broken ground states, which do not depend on the microscopic details of the model in the limit of large regions. Finally, we discuss some consequences of the Kramers-Wannier duality, which relates the ordered and disordered phases of the Ising model, and we explain why, counterintuitively, no explicit relations between those phases are found at the level of entanglement.

DOI: 10.1007/JHEP02(2025)025

Source: https://link.springer.com/article/10.1007/JHEP02(2025)025

来源：科学网  小柯机器人