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Compression theory for inhomogeneous systems.

Doruk Efe Gökmen1,2,3,4, Sounak Biswas5, Sebastian D Huber6

  • 1Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland. gokmen@uchicago.edu.

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|November 25, 2024
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Summary
This summary is machine-generated.

Compression theory extracts key data from complex systems on irregular structures. This enables effective theories for systems lacking translational invariance, revealing exotic critical points.

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Area of Science:

  • Complex Systems Physics
  • Data-Driven Computational Methods
  • Condensed Matter Theory

Background:

  • Complex systems often involve interacting degrees of freedom on inhomogeneous graphs.
  • Lack of translational invariance challenges traditional theoretical tools like the renormalization group.
  • Advances in data availability and computational methods offer new avenues for analysis.

Purpose of the Study:

  • To develop a method for extracting relevant degrees of freedom in arbitrary geometries.
  • To create efficient numerical tools for building effective theories from data.
  • To apply this method to complex physical systems lacking translational invariance.

Main Methods:

  • Utilizing compression theory for degree of freedom extraction.
  • Developing efficient numerical tools for data-driven theory construction.
  • Applying the method to strongly correlated systems on quasicrystals and antiferromagnetic systems on random graphs.

Main Results:

  • Demonstrated successful extraction of relevant degrees of freedom in arbitrary geometries.
  • Discovered an exotic critical point with broken conformal symmetry in a quasicrystal system.
  • Applied the method to non-bipartite random graphs, showing its applicability where periodicity is absent.

Conclusions:

  • Compression theory provides a powerful framework for analyzing complex systems lacking translational invariance.
  • The developed numerical tools enable the construction of effective theories directly from data.
  • This approach opens new possibilities for understanding universal physical behavior in diverse, complex systems.