标题： 物理信息归一化群流 显示英文标题

标题： Physics-informed renormalisation group flows

摘要： 强关联系统物理学提供了许多引人入胜的物理挑战，例如竞争秩序或动态复合自由度的出现。 通常，解决这些物理挑战在计算上是困难的，但可以通过用动态自由度来表述并在物理基态附近进行展开来大大简化。 重要的是，这种表述不仅减少了或最小化了计算挑战，还促进了对所涉及的物理机制的访问。 寻找动态自由度和物理基态的任务可以在具有流动场的功能性重整化群方法中系统地解决，该方法既容纳了涌现的复合体，也容纳了物理基态。 在本工作中，我们使用这种方法来建立物理信息重整化群流（PIRG流）：场空间中的尺度依赖坐标变换会引发涌现的复合体，而有效作用量的相应流会产生一组目标作用量，这些作用量是在这些涌现的复合体场中表述的。 对RG流的这种新观点在概念和计算应用方面都有很大的潜力：首先，PIRG流允许系统地搜索动态自由度和相应的基态，这会导致展开方案的最快收敛，从而最小化计算工作量。 其次，在给定的展开方案中，通过优化给定近似中的物理内容，可以进一步减少剩余计算任务的解决难度。 第三，PIRG流的最大可变性可用于减少在给定近似下求解流的分析和数值工作量。 显示英文摘要

摘要： The physics of strongly correlated systems offers some of the most intriguing physics challenges such as competing orders or the emergence of dynamical composite degrees of freedom. Often, the resolution of these physics challenges is computationally hard, but can be simplified enormously by a formulation in terms of the dynamical degrees of freedom and within an expansion about the physical ground state. Importantly, such a formulation does not only reduce or minimise the computational challenges, it also facilitates the access to the physics mechanisms at play. The tasks of finding the dynamical degrees of freedom and the physical ground state can be systematically addressed within the functional renormalisation group approach with flowing fields which accommodates both, emergent composites as well as the physical ground state. In the present work we use this approach to set up physics-informed renormalisation group flows (PIRG flows): Scale-dependent coordinate transformations in field space induce emergent composites, and the respective flows for the effective action generate a large set of target actions, formulated in these emergent composite fields. This novel perspective on RG flows bears a great potential both for conceptual as well as computational applications: to begin with, PIRG flows allow for a systematic search of the dynamical degrees of freedom and the respective ground state that leads to the most rapid convergence of expansion schemes, thus minimising the computational effort. Secondly, the resolution of the remaining computational tasks within a given expansion scheme can be further reduced by optimising the physics content within a given approximation. Thirdly, the maximal variability of PIRG flows can be used to reduce the analytic and numerical effort of solving the flows within a given approximation.