Abstract：The strongly correlated problem in many body physics can be mapped to a weak interacting problem with gauge symmetry. The essential issue for this gauge theory is how to find a gauge fixing condition which is consistent with the local constraint in the strongly correlated system. This was failed in previous studies of the gauge theory. Recently, we developed a consistent gauge theory in the slave boson representation of the strongly correlated fermion system. Using the Faddeev-Popov procedure, the consistent gauge conditions for general gauge theories with Dirac’s first-class constraints were found more than fifty years ago. The BRST symmetry plays a role of the guiding principle in this procedure. We show that it can be used to the strongly correlated system around the atomic limit. But the constraints in the ordered phases of the slave boson representation are Dirac’s second-class ones and so the new method needs to be developed. Fortunately, guided by the BRST symmetry, we established a consistent gauge theory for the ordered phases. Applying to the t-J model, the gauge theory is a theory of the spinon and holon weakly coupled to a dynamic gauge field. We then use Feynman’s diagram technique to perturbatively study the normal state which is believed describing the strange metal physics for the cuprate. Calculations for the other phases such as the pseudogap and superconducting phases are in progress.

报告人简介：虞跃，1982年大学毕业于浙江大学物理系。1987年在浙江大学获理论物理博士学位。1987年底至1992年6月在中国科学院高能物理所和理论物理所做博士后。 1992年至2013年任中国科学院理论物理所副研究员、研究员，期间曾在英国Warwick大学、美国Utah大学和Delaware大学作较长期访问。2013年至今为复旦大学物理系教授, 现任复旦大学场论和粒子理论中心主任。曾任中国科学院理论物理研究所副所长，获香港求是基金会青年科学家奖, 2000年获国家杰出青年基金资助。主要从事凝聚态强关联理论和拓扑物态理论研究，例如，分数量子霍尔效应、强关联电子系统、分数排斥统计、超对称性的量子模拟、Rarita-Schiwinger semimetal和普适拓扑量子计算等。