Field theoretic and holographic approaches to strongly correlated quantum many-body systems

强相关量子多体系统的场论和全息方法

• 批准号: 341439-2013
• 负责人: Lee, SungSik
• 金额: $ 1.82万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=527308
• 关键词: Field; theoretic; holographic; approaches; strongly

Condensed matters systems, that include metals and insulators, are made of many particles of the order of ten to the twenty three. Behaviors of individual particles are governed by the well established law of physics, quantum mechanics. It is straightforward to apply quantum mechanics to condensed matter systems if interactions between particles are weak. In weakly interacting systems, one can predict behaviors of a whole system by studying individual particles one by one because correlations between particles are weak. However, such `single-particle approaches' drastically fail when there are strong interactions and correlations between particles. This turns out to be the case in many recently discovered materials, such as high temperature superconductors. In those materials, one can not understand physical properties without understanding the system as a whole because behaviors of individual particles are strongly affected by other particles. It is generally impossible to solve those problems from first-principle calculations because there are so many degrees of freedom that are entangled with each other through strong interactions. On the other hand, strongly correlated systems often show new types of unexpected collective phenomena as a result of non-trivial quantum mechanical entanglements between particles. For example, electric current flows without any resistance even in the presence of impurities in superconducting state, and conductance is quantized independent of details of samples in quantum Hall states. When a condensed matter system shows distinct collective behaviors, it is a sign that the system is in a new phase of matter. My research is concerned about theoretically understanding novel collective phenomena that arise in strongly correlated quantum many-body systems. I focus on a small set of collective degrees of freedom in order to capture essential phenomena in an efficient way instead of trying to understand all the microscopic details in many-body systems. The present research will not only help us to improve our fundamental understanding of strongly correlated quantum many-body systems, but also to use various novel materials for applications, such as information technology.

包括金属和绝缘子在内的冷凝物质系统由十三到十三个阶的许多粒子制成。单个颗粒的行为受物理学良好的量子力学定律的控制。如果颗粒之间的相互作用较弱，则将量子力学应用于凝结物质系统是很简单的。在弱相互作用的系统中，人们可以通过一个一个一个一个一个一个研究单个粒子来预测整个系统的行为，因为粒子之间的相关性很弱。但是，当粒子之间存在强相互作用和相关性时，这种“单粒子方法”会大大失败。事实证明，在许多最近发现的材料（例如高温超导体）中就是这种情况。在这些材料中，人们无法理解物理特性而不理解整个系统，因为单个颗粒的行为受到其他颗粒的强烈影响。通常不可能从第一原则计算中解决这些问题，因为有如此多的自由度通过强烈的互动彼此纠缠在一起。另一方面，由于粒子之间的非平凡量子机械纠缠，紧密相关的系统通常会显示出新型的意外集体现象类型。例如，即使在超导状态下具有杂质的情况下，电流流也没有任何阻力，并且在量子大厅状态下的样品细节中对电导进行量化。当冷凝物质系统显示出不同的集体行为时，这表明该系统处于新阶段。我的研究关注理论上理解在密切相关的量子多体系统中出现的新型集体现象。我专注于一系列集体的自由度，以便以有效的方式捕获基本现象，而不是试图理解多体系统中的所有微观细节。本研究不仅将帮助我们提高对密切相关的量子多体系统的基本理解，而且还可以使用各种新颖的材料进行应用，例如信息技术。