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Related Concept Videos

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Dimensionless Groups in Fluid Mechanics

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Related Experiment Videos

Uncomputably complex renormalisation group flows.

James D Watson1, Emilio Onorati2, Toby S Cubitt2

  • 1Department of Computer Science, University College London, London, UK. ucapjdj@ucl.ac.uk.

Nature Communications
|December 9, 2022
PubMed
Summary
This summary is machine-generated.

Renormalization group (RG) methods analyze many-body systems. A new RG map for an undecidable system shows a complex, unpredictable flow, even though each step is computable.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information
  • Computational Physics

Background:

  • Renormalization group (RG) methods are crucial for analyzing many-body systems by coarse-graining system descriptions and generating parameter space flows.
  • Recent studies indicate that critical physical properties, like spectral gaps and phase diagrams, may be fundamentally undeterminable using these methods.
  • The concept of undecidability in physical systems poses significant challenges to traditional analytical techniques.

Purpose of the Study:

  • To construct a rigorous renormalization group map for a known undecidable many-body system.
  • To investigate the nature and predictability of the renormalization group flow in this complex system.
  • To rigorously analyze the computability and convergence properties of the constructed RG map.

Main Methods:

  • Development of a rigorous renormalization group map tailored to a specific undecidable many-body system.
  • Mathematical proof of the computability of each individual step within the RG map.
  • Analysis of the convergence of the RG map to its fixed points.
  • Characterization of the overall complexity and predictability of the resulting RG flow.

Main Results:

  • A rigorous RG map was successfully constructed for the specified undecidable many-body system.
  • It was proven that each step of the RG map is computable.
  • The RG map was shown to converge to the correct fixed points.
  • The overall RG flow generated by this map was demonstrated to be uncomputable and highly complex, exceeding previously observed chaotic behaviors.

Conclusions:

  • The study demonstrates an extreme form of unpredictability in renormalization group flows for certain many-body systems.
  • This uncomputability goes beyond previously understood chaotic dynamics, highlighting fundamental limitations.
  • The findings have significant implications for the theoretical analysis and predictability of complex quantum systems.