Quantum criticality: coupled renormalization of electrons and order parameter fluctuations

在这个项目中，我们研究了相互作用费米系统中的几种类型的量子相变，即对称相和对称性自发破缺的有序相之间的相变。其中包括金属中的向列相转变，半金属中的正常到超流体转变，以及(相对论)Thirring模型中的手征对称破缺。主要焦点将放在(2+1)维系统上。我们特别感兴趣的是有效序参理论(Hertz-Millis理论)不能正确描述低能行为的系统。泛函RG将被用来分析电子激发和序参数涨落的耦合系统，即费米子和玻色子将同时积分出来。我们将尝试推导和求解一组流动方程，它适当地处理在量子相变附近出现的所有纠缠奇点。我们将访问相图的所有区域，包括对称破缺区域和受非高斯涨落支配的区域。我们将充分利用功能RG的可能性，允许真正的功能流，例如全参数势流，捕捉具有任意场幂的顶点。

In this project we study several types of quantum phase transitions in interacting Fermi systems, between a symmetric phase and an ordered phase with spontaneously broken symmetry. These include the nematic transition in metals, a normal to superfluid transition in semi-metals, and chiral symmetry breaking in the (relativistic) Thirring model. The main focus will be on (2+1)-dimensional systems. We are particularly interested in systems for which an effective order parameter theory truncated at quartic order in the fields (Hertz-Millis theory) does not describe the low energy behavior correctly. The functional RG will be used to analyze the coupled system of electronic excitations and order parameter fluctuations, that is, fermions and bosons will be integrated out simultaneously. We will try to derive and solve a set of flow equations which properly treats all the entangled singularities appearing near the quantum phase transition. We will access all regions of the phase diagram, including the symmetry-broken regime and regimes governed by non-Gaussian fluctuations. We will take full advantage of the possibilities of the functional RG by allowing also for truly functional flows, such as flows of the fullo rder parameter potential, capturing vertices with arbitrary powers of the fields.