AdS/CFT对偶在强耦合费米系统中的应用

How to understand the strongly coupled fermions and search for an organizing principle behind them are some of the most challenging problems in theoretical physics. The AdS/CFT duality can relate a classical gravity theory in a weakly curved AdS spacetime to a strongly coupled quantum field theory, which provide new insights and methods for understanding strongly coupled systems. First, we will explore the properties of the holographic fermions that the ground state entropy vanishes, the fermions with backreactions and the holgraphic fermions with lattices. In addition, we also focus on how to understand the "2kF" singularities in condensed matter theory in term of AdS/CFT duality. In order to expose particle-hole pairs, we will introduce the effects from string theory. We expect that one can find "2kF" sigularities in strongly coupled fermionic systems. Finally, we will explore the propertis of the OTU model proposed by Takayanagi et. al.. We will propose an OTU holographic superconductor model and study the behavior of OTU model in the presence of magnetic field to confirm the existence of the Fermi surfaces. Specially, we will study the relation between the hidden Fermi surfaces revealed by holographic entanglement entropy and the visible Fermi surface probed by the probe fermions.

如何理解强耦合多体费米系统以及寻找其背后的组织原则是当前理论物理最具挑战性的问题之一。AdS/CFT 对偶作为一种强弱耦合的对偶，为理解强耦合系统提供了新的视角和方法。在本项目中，将首先研究零基态熵费米系统的特征，包括有限温度的情况，磁场效应，电导率的计算和如何将零基态熵全息费米系统和现实凝聚态模型关联起来。接着，将构建反作用全息费米系统和研究全息格点费米系统。此外，本项目的另一个重点内容是如何应用AdS/CFT对偶理解凝聚态系统中的"2kF"奇点问题。为了暴露粒子-空穴对，将引入了弦理论以及量子引力效应。期待通过计算密度关联函数找到强耦合费米系统的"2kF"奇点，并与实验观察结果进行比较。在全息纠缠熵方面，研究Takayanagi等人提出的OTU模型的特点，构建OTU 全息超导体，研究考虑磁场效应时OTU 模型的行为，以确认费米面的存在，也研究隐藏费米面和可视费米面的关系。

该项目顺利执行了相关研究内容并取得了很好的效果，完成预期目标。具体如下：1）研究内容方面：研究了利弗席兹(Lifshitz)几何背景下的费米谱函数；波恩-英费尔德反德西特(Born–Infeld AdS)黑膜几何背景的费米谱函数；系统研究了均匀无序模型（包括质量子引力，空间线性依赖的线性轴子场及Q格点结构）的费米谱函数；构建质量子全息超导体模型和全息Q格点超导体模型；系统研究了全息金属绝缘体及其相变行为，包括全息类模特金属绝缘相变、全息派尔斯金属绝缘相变及其诱导的电荷密度波(CDW)；全息奇异金属的输运性质。这些工作为利用全息技术研究凝聚态物理提供新的视角和理解。2）文章发表方面：完成SCI学术论文20篇和学术专著一部，包括一篇Phys.Rev.Lett.论文。3）学生培养方面：在读研究生2人。