权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

New Frontiers on Entanglement Measures in the Quantum sine-Gordon Model

量子正弦戈登模型中纠缠测量的新前沿

基本信息

批准号：
EP/W007045/1
负责人：
Olalla Castro-Alvaredo
金额：
$ 7.56万
依托单位：
City, University of London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2022
资助国家：
英国
起止时间：
2022 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FW007045%2F1
关键词：
New Frontiers Entanglement Measures Quantum

项目摘要

Branch Point Twist Fields are a leading tool in the context of the analytic computation of entanglement measures in 1+1D quantum field theory (QFT). Their usefulness follows from the relationship between entanglement measures and correlation functions of branch point twist fields. More precisely, in 1+1D entanglement measures can be expressed in terms of n-point functions of branch point twists fields, where n is the number of boundary points between the regions A and B whose mutual bipartite entanglement is being evaluated. Since this approach was introduced for massive theories in 2007, branch point twist fields have been employed in multiple contexts to either study features of entanglement (both at and away from equilibrium) or to construct building blocks of generic entanglement measures (i.e. form factors). The PI has been involved in much of this work. Despite substantial activity, integrable QFTs with non-diagonal scattering have been much less studied due to the well-known complexities of form factor computations. In particular, for the most paradigmatic non-diagonal integrable QFT, the sine-Gordon model, there have been only two publications in recent years, both involving the PI. The first in 2009 was a study of the repulsive regime of the theory (where the particle spectrum is particularly simple), and more recently, in the current year, a more ambitious study for the full range of values of the coupling (hence a much more involved particle spectrum) was carried out. This recent work was in collaboration with David X. Horvath (SISSA, Italy). The current proposal follows organically from this recent collaboration which has created an opportunity for a much more ambitious study of the problem. In particular, our joint expertise, puts us in the best position to consider one of the most recent entanglement measures of interest, namely the symmetry resolved entanglement entropy, in the sine-Gordon model. It has been recently discovered that in the presence of an internal symmetry, the structure of the reduced density matrix in terms of which all entanglement measures are constructed, is highly predictable and regular. In general, it is block-diagonal, which block-sizes relating to the underlying symmetry. This also means that each block makes a contribution to entanglement measures and that those individual contributions can be computed as quantities of particular interest. Following this observation, Horváth and Calabrese (2020) have developed a new form factor programme for a generalized branch point twist field whose correlators give the block contributions to entanglement. One of the main objectives of this project is to compute the form factors of these new branch point twist fields in the sine-Gordon model, study their analytical properties, hence the analytical properties of the symmetry resolved entanglement. This project requires advanced knowledge of the technicalities involved in such types of computation, which the PI and collaborators have an excellent track record of.

分支点扭曲场是1+ 1维量子场论中纠缠测度解析计算的重要工具。它们的有用性来自于分支点扭曲场的纠缠度量和关联函数之间的关系。更精确地说，在1+1D中，纠缠度量可以用分支点扭曲场的n点函数来表示，其中n是区域A和B之间的边界点的数量，区域A和B的相互二分纠缠被评估。自从这种方法在2007年被引入到大质量理论中以来，分支点扭曲场已经在多种背景下被用来研究纠缠的特征（无论是在平衡态还是远离平衡态），或者构建通用纠缠度量的构建模块（即形状因子）。PI参与了大部分工作。尽管有大量的活动，但由于形状因子计算的众所周知的复杂性，具有非对角散射的可积QFT的研究要少得多。特别是，对于最典型的非对角可积QFT，sine-Gordon模型，近年来只有两个出版物，都涉及PI。2009年的第一项研究是对该理论的排斥机制的研究（其中粒子谱特别简单），最近，在本年度，对耦合的全范围值进行了更雄心勃勃的研究（因此涉及更多的粒子谱）。最近的这项工作是与大卫X合作完成的。Horvath（西萨，意大利）.目前的建议有机地遵循了最近的合作，这为对这一问题进行更雄心勃勃的研究创造了机会。特别是，我们的联合专业知识，使我们在最好的位置，考虑最近的纠缠感兴趣的措施之一，即对称解决纠缠熵，在正弦戈登模型。最近发现，在存在内部对称性的情况下，构造所有纠缠度量的约化密度矩阵的结构是高度可预测的和规则的。一般来说，它是块对角的，它的块大小与潜在的对称性有关。这也意味着每个块都对纠缠度量做出贡献，并且这些单独的贡献可以作为特别感兴趣的量来计算。根据这一观察，Horváth和Calabrese（2020）为广义分支点扭曲场开发了一个新的形状因子方案，该扭曲场的双折射子为纠缠提供了块贡献。本项目的主要目标之一是计算sine-Gordon模型中这些新的分支点扭曲场的形状因子，研究它们的解析性质，从而研究对称分辨纠缠的解析性质。这个项目需要对这类计算所涉及的技术细节有深入的了解，PI和合作者在这方面有着良好的记录。