Information geometric approach to the renormalisation group

TL;DR

This paper introduces an information geometric framework for the renormalisation group, modeling it as quantum channels and quantifying information loss through distinguishability of thermal states, with applications to infinite lattices.

Contribution

It develops a novel geometric formulation of the RG as quantum channels and introduces functions to measure information loss along RG flows.

Findings

Quantifies information loss using distinguishability of thermal states.

Defines a family of functions based on two-point correlation functions that decrease along RG flows.

Extends the geometric approach to infinite lattice systems.

Abstract

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.