Hyperscaling of Fidelity and Operator Estimations in the Critical Manifold

TL;DR

This paper formulates the renormalization group as a quantum channel in QFTs, deriving hyperscaling relations at criticality that enable replacing complex theories with their fixed-point limits for expectation value calculations.

Contribution

It introduces a novel approach to analyze QFTs using quantum channels, establishing hyperscaling relations that facilitate simplified computations at critical points.

Findings

Derived hyperscaling relations at criticality.

Identified when QFTs can be replaced by fixed-point theories.

Enhanced methods for numerical and analytical critical model analysis.

Abstract

By formulating the renormalization group as a quantum channel acting on density matrices in Quantum Field Theories (QFTs), we show that ground-state expectation values of observables supported on slow momentum modes can be approximated by their averages on the fixed-point theories to which the QFTs flow. This is done by studying the fidelity between ground states of different QFTs and arriving at certain hyperscaling relations satisfied at criticality. Our results allow for a clear identification of cases in which one can replace a QFT by its scale-invariant limit in the calculation of expectation values, opening the way for a range of applications, including the improvement of numerical and analytical methods used to tackle the costly computer simulation of critical models.