高温超导是凝聚态物理最重要的研究领域之一。经过二十多年的实验和理论研究，其基本物理机制仍然很不清楚。高温超导之所以难以理解，重要原因是它的相图非常复杂，随掺杂浓度的变化，可能的基态包括反铁磁、超导、nematic、条纹等，这些长程序不是独立的，而是互相影响的。事实上，超导序和其它序之间存在较强的竞争关系，在一定条件下可以共存，这导致了诸多奇异的物理现象。研究序竞争有重要的科学意义，能帮助人们理解高温超导的很多反常行为，对最终揭示高温超导的基本物理机制有重要的推动作用。本项目研究高温超导中的序竞争，主要是超导－反铁磁竞争和超导－nematic竞争，因为这两种序竞争的存在已得到越来越多实验证据的支持。我们将对相关的众多实验现象进行分析，建立能较好地描述高温超导中序竞争的有效场论模型，利用量子场论和多体理论的解析、数值计算方法，系统、深入地研究序竞争的物理性质和它导致的各种反常物理效应。

High temperature superconductivity is one of the most important research fields in condensed matter physics. Despite the extensive experimental and theoretical investigations in the past two decades, the microscopic mechanism of high temperature superconductivity remains unsolved. One reason for this situation is that high temperature superconductor has a very complicated phase diagram. Depending on the value of doping concentration, its ground state could exhibit antiferromagnetic order, superconducting order, nematic order, or stripe order. These orders are definitely not independent, but have significant influence on each other. In particular, the superconducting order strongly competes, and under certain conditions coexists, with the other three orders, which in turn leads to highly unusual properties.It is very interesting to systematically study competing orders, since it can help understand many anomalous behaviors of high temperature superconductors and reveal the microscopic pairing mechanism. We plan to investigate a number of problems regarding competing orders in high temperature superconductors. Our focus will be on the competition between superconducting and antiferromagnetic orders, and the competition between superconducting and nematic orders, because there have been increasing evidence for the existence of these two competitive phenomena. We shall analyze the relevant experimental facts about competing orders, and construct an effective field theory to properly describe the competition and coexistence between different orders. We then study this effective theory by means of various quantum field-theoretic and many-particle techniques. Based on these studies, we can carefully explore the essential properties of competing orders and understand the remarkable behavior caused by competing orders.