重正化群的信息几何方法
Information geometric approach to the renormalisation group
摘要：
我们提出了一个一般配方的重正化群作为一个家庭的量子信道连接微观物理世界的可观察世界在一定尺度上。通过赋予量子态集合一个操作性激发的信息几何，我们导出了具有相应度量几何的哈密顿量空间。由此产生的结构允许一个量化的信息损失沿RG流的热状态的可扩展性。特别是，我们引入了一个家庭的功能，表达的两点关联函数，这是不增加沿流动。其中，我们研究了流的速度，并将其推广到无限格。
英文摘要：
We propose a general formulation of the renormalisation group as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally motivated information geometry, we induce the space of Hamiltonians with a corresponding metric geometry. The resulting structure allows one to quantify information loss along RG flows in terms of the distinguishability of thermal states. In particular, we introduce a family of functions, expressible in terms of two-point correlation functions, which are non increasing along the flow. Among those, we study the speed of the flow, and its generalization to infinite lattices.
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