We present a bosonization method to study generic low energy behavior of gauge systems with finite chemical potential in 2+1 dimensions. Benefit from the existence of gap (e.g. Gribov gap) in gauge systems at low energy, the fermion fields can be explicitly bosonized by new gauge fields. When chemical potential of the gauge systems is introduced, we find that topological terms (such as Chern-Simons term in 2+1D) as constraints inevitably emerge at low energy. The fermion sign problem at finite chemical potential and its deep connection to the Chern-Simons theories are discussed. The Wilson's criteria of confinement in pure gauge theories is generalized to finite chemical potential case. The chemical potential dependence of physical quantities at strong coupling are explicitly calculated, including the expectation value of the Wilson loop, the confining potential and the confined/deconfined transition temperature. The bosonization puts discussions on chiral symmetry breaking and confined/deconfined transition on an equal footing, so it is suitable for the study of the subtle interplay between them. We find that the chiral symmetry breaking is a necessary (not sufficient) condition for the confinement in 2+1D, and argue that the confined/deconfined phases are not characterized by any local symmetries but distinguished by their non-local topologies. The low energy modes of the strongly coupled gauge systems in a non-symmetry breaking phase is also discussed. The results of the paper can be widely applied to real strongly coupled gauge systems, e.g. high-temperature superconductor and quantum chromodynamical systems in 2+1 dimensions.
Bosonization duality in 2+1 dimensions and critical current correlation functions in Chern-Simons $U(1)\times U(1)$ Abelian Higgs model
虽然$U(1)\times U(1)$对称希格斯理论的相结构仍在争论中，但最近证明了该理论的一个附加Chern-Simons项的版本经历了二级相变[V. Shyta，J. van den Brink和F. S. Nogueira，Phys. Rev. Lett. 127，045701（2021）]。这个理论是对偶的拓扑场论的无质量费米子具有两个规范场。在这里，我们详细阐述了这种二重性的几个方面，重点是临界电流的放大器和玻色化二重性所反映的临界点的性质。与$U(1)\times U(1)$对称性和拓扑电流相关联的电流子被证明是一致的，直到一个普遍的前因子，我们发现这是相同的$U(1)$和$U(1)\times U(1)$拓扑希格斯理论。已建立的对偶性提供了另外一种方法来证实玻色子陈-西蒙斯$U(1)\times U(1)$希格斯模型中存在临界点的说法：对费米子对偶模型的施温格-戴森分析表明，没有动力学质量产生发生。如果作用量中没有陈-西蒙斯项，理论就不能这样说。
Emergent Gauge Flux in Mixed QED$_3$ with Flavor Chemical Potential: Implications for Magnetized U(1) Dirac Spin Liquids
The University of Hong Kong（香港大学）；HK Institute of Quantum Science & Technology（香港量子科学院）；State Key Laboratory of Optical Quantum Materials（光学量子材料国家重点实验室）；University of Cologne（科隆大学）；University of Utah（犹他大学）；Kavli Institute for Theoretical Physics（卡弗里理论物理研究所）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；French American Center for Theoretical Science（法美理论科学中心）；CNRS（法国国家科学研究中心）；KITP（卡弗里理论物理研究所）；Canadian Institute for Advanced Research（加拿大高级研究院）
