I am posing this question with condensed matter systems in mind. **Is it, in principle, possible to obtain emergence using the renormalization group (RG)?** I read in X.-G. Wen's book (Quantum Field Theory of Many-Body systems) that "*we cannot use the renormalization group approach to obtain the emergence of qualitatively new phenomena*" (Sec. 3.5.4 on page 110). It seems to me that the statement should have been something like RG, **in practice**, cannot be used to capture emergence. Or, more precisely, local perturbative RG schemes are not suited for capturing emergence.

Here is what confuses me: if emergence is nothing but the statement that the low-energy degrees of freedom may not be the same as the high-energy, microscopic degrees of freedom in a theory, then **in principle** RG should be able to capture emergence, right?