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

凝聚态物质系统，包括金属和绝缘体，是由许多10的23次方的粒子组成的。单个粒子的行为受公认的物理学定律——量子力学的支配。如果粒子之间的相互作用很弱，将量子力学应用于凝聚态系统是很简单的。在弱相互作用系统中，由于粒子之间的相关性很弱，人们可以通过逐个研究单个粒子来预测整个系统的行为。然而，当粒子之间存在强烈的相互作用和相关性时，这种“单粒子方法”就会彻底失败。这在许多最近发现的材料中都是如此，比如高温超导体。在这些材料中，如果不了解整个系统，就无法了解物理性质，因为单个粒子的行为受到其他粒子的强烈影响。通常不可能通过第一原理计算来解决这些问题，因为有太多的自由度通过强相互作用相互纠缠在一起。另一方面，强相关系统经常表现出意想不到的新型集体现象，这是粒子之间非平凡量子力学纠缠的结果。例如，在超导状态下，即使有杂质存在，电流也不会产生任何阻力；在量子霍尔状态下，电导率的量子化与样品的细节无关。当一个凝聚态系统表现出明显的集体行为时，这是系统处于物质新阶段的标志。我的研究关注从理论上理解在强相关量子多体系统中出现的新的集体现象。我专注于一小部分集体自由度，以便以一种有效的方式捕捉基本现象，而不是试图理解多体系统中的所有微观细节。目前的研究不仅有助于我们提高对强相关量子多体系统的基本理解，而且还可以将各种新型材料用于信息技术等应用。

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.