Competing order parameters and flows into phases with broken symmetries

对竞争有序化倾向的理解仍然是现代凝聚态物理学中最相关的问题之一。在这个项目中，我们使用功能RG来研究这种竞争，无论是在二维关联费米子模型的上面还是在二维关联费米子模型的破缺相中，总体目标是确定相边界，序参数对称性和幅度，并理解低能行为。前向和umklapp散射项在RG流的二维哈伯德模型以上和以下的破环尺度。为此，我们想比较和联合收割机的技术和见解，在我们的小组在费米和玻色子功能RG流在过去三年中，为了跟踪流到最低尺度，从而确定接近半满的相图，涉及的重要问题包括：（1）确定费米子相互作用的哪些部分是顶点（对应于交换玻色子）需要包括在不同的尺度，（2）跟踪动量和频率依赖的自能，Yukawa型顶点函数和四费米子项，以及功能依赖的局域势在破缺制度，（3）保证流函数渐近满足Ward恒等式。此外，我们将使用我们的方法更深入地研究现代关联电子系统的其他例子，例如非常规超导体或拓扑电子态。

The understanding of competing ordering tendencies remains one of the most relevant questions in modern condensed matter physics. In this project we use the functional RG to study this competition, both above and in the symmetry-broken phase of two-dimensional correlated fermion models, with the overall goal of determining phase boundaries, order parameter symmetries and magnitudes, and understanding the low-energy behaviour.A major aim is a controlled analysis of the interplay of magnetic, superconducting, forward and umklapp scattering terms in the RG flow for the two-dimensional Hubbard model both above and below the symmetry-breaking scale. To this end, we want to compare and combine the techniques and insights obtained in our group on fermionic and bosonic functional RG flows during the past three years, in order to follow the flow to the lowest scales and thus determine the phase diagram close to half-filling.Important issues involved in this include (1) determining which parts of the fermionic interaction vertex (corresponding to exchange bosons) need to be included at different scales, (2) tracking the momentum and frequency dependence of self-energies, Yukawa-type vertex functions and four-fermion terms, as well as the functional dependence of local potentials in the symmetry-broken regime, and (3) ensuring that the flowing functions asymptotically fulfill the Ward identities. Furthermore, we will use our method to examine other examples of modern correlated electron system, such as unconventional superconductors or topological electron states in more depth.