Emergent electrostatics in planar XY spin models: The bridge connecting topological order with broken U(1) symmetry

Topological phases have been a central focus of condensed-matter physics for over 50 years.  Along with many experimental applications, they have provided much intellectual interest due to their characterization via some form of topological ordering, as opposed to the symmetry-breaking ordering of conventional continuous phase transitions.  This distinction is most subtle in the case of the Berezinskii—Kosterlitz—Thouless (BKT) transition as its experimental realizations appear to break U(1) symmetry at low temperature.  It also presents two further paradoxes: i) its prototypical short-range interacting planar XY spin model behaves as an emergent long-range interacting electrolyte; ii) its topological ordering is not accompanied by a topological nonergodicity within the BKT picture.  This data deposit supports a review paper that addresses these three interconnected questions.  In particular, it provides the simulation data that supports the concept of topologic..., , # Emergent electrostatics in planar XY spin models: The bridge connecting topological order with broken U(1) symmetry

Dataset DOI: [10.5061/dryad.v15dv427n](10.5061/dryad.v15dv427n)

## Description of the data and file structure

This data deposit contains simulation data that supports the paper (published by Michael F. Faulkner) entitled: *Emergent electrostatics in planar XY spin models: the bridge connecting topological order with broken U(1) symmetry*.  We refer to this paper as *Emergent electrostatics* below.

The majority of the simulation data contained in the present deposit is that used to support the concept of topological nonergodicity throughout the low-temperature phase of planar XY spin models.

Simulation data that supports the concept of broken *U*(1) symmetry (at low temperature) is reproduced (within the above paper) from another research article.  This data was stored in the University of Bristol data repository, data.bris, with DOI 10.5523/bris.3ov1rl6xtshwv2iuixrb...,

拓扑相（Topological phases）在过去五十余年间始终是凝聚态物理的核心研究焦点之一。伴随诸多实验应用，这类体系凭借基于拓扑序的表征方式——区别于传统连续相变的对称性破缺序——引发了大量学术研究兴趣。这一区分在贝雷津斯基-科斯特利茨-索利斯（Berezinskii–Kosterlitz–Thouless, BKT）相变中体现得最为微妙：其实验实现体系看似在低温下破坏了U(1)对称性。该相变还存在另外两个反直觉的问题：其一，其原型短程相互作用平面XY自旋模型会表现出涌现长程相互作用电解质的特性；其二，在BKT相变的理论框架下，其拓扑序并未伴随拓扑非各态历经性。本数据集旨在支撑一篇针对上述三个相互关联问题的综述论文，具体而言，它提供了用于验证拓扑相关概念的模拟数据……
# 平面XY自旋模型中的涌现静电学：连接拓扑序与破缺U(1)对称性的桥梁

数据集DOI：[10.5061/dryad.v15dv427n]

## 数据与文件结构说明
本数据集收录的模拟数据，用于支撑Michael F. Faulkner发表的题为《平面XY自旋模型中的涌现静电学：连接拓扑序与破缺U(1)对称性》的论文，下文简称《涌现静电学》。
本数据集的绝大多数模拟数据，用于验证平面XY自旋模型低温相内的拓扑非各态历经性相关概念。
用于支撑低温下破缺U(1)对称性相关概念的模拟数据，已在上述论文中从另一篇研究论文中复刻引用。该部分数据此前存储于布里斯托大学数据仓储平台data.bris，其DOI为10.5523/bris.3ov1rl6xtshwv2iuixrb...