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，在对称相和具有自发破缺对称性的有序相之间。这些包括金属中的超临界转变，半金属中的正常到超流转变，以及（相对论）Thirring模型中的手征对称性破缺。主要的重点将放在（2+1）维系统。我们特别感兴趣的系统，有效的序参量理论截断在四阶的领域（赫兹-米利斯理论）不正确地描述低能量的行为。泛函RG将用于分析电子激发和序参量涨落的耦合系统，即同时积分出费米子和玻色子。我们将尝试导出并求解一组流方程，它能恰当地处理出现在量子相变附近的所有纠缠奇点。我们将访问相图的所有区域，包括非高斯波动的破缺区域和区域。我们将充分利用功能RG的可能性，也允许真正的功能流，如流的fullorder参数的潜力，捕捉与任意权力的领域的顶点。

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.