Inverse Renormalization Group in Quantum Field Theory

Abstract

We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing down effect in calculations pertinent to criticality. Given configurations of the two-dimensional ${\varphi }^4$ scalar field theory on sizes as small as $V=8^2$, we apply the inverse transformations to produce rescaled systems of size up to $V^{\prime }=512^2$ which we utilize to extract two critical exponents. We conclude by discussing how the approach is generally applicable to any method that successfully produces configurations from a statistical ensemble and how it can give novel insights into the structure of the renormalization group.

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• Quantum field theories, Markov random fields and machine learning
• Reducing finite-size effects with reweighted renormalization group transformations
• Machine learning with quantum field theories