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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Materials Science

Background:

  • Standard topological classification may not capture all quantum phenomena.
  • Lorentz invariance breakdown is crucial for understanding exotic quantum states.
  • Anisotropic behavior in topological models requires further investigation.

Purpose of the Study:

  • To investigate topological models beyond standard classification, focusing on Lorentz invariance breakdown.
  • To analyze anisotropic quantum critical behavior in three-dimensional topological models.
  • To characterize topological surface states and critical exponents in novel materials.

Main Methods:

  • Numerical calculations of penetration length for zero-energy surface states.
  • Study of a generalized Weyl semimetal model using a modified Dirac equation.
  • Analysis of topological surface states, including Fermi arcs and Hopf insulators.

Main Results:

  • Computed anisotropic correlation length critical exponent [Formula: see text] in 3D topological models.
  • Developed an approach to capture anisotropic critical exponents in topological insulators.
  • Observed unusual values for [Formula: see text] and dynamic critical exponent z in Hopf insulators.

Conclusions:

  • Proposed a new scaling relation [Formula: see text] for critical exponents in Hopf insulators.
  • Derived an anisotropic quantum hyperscaling relation.
  • Demonstrated the importance of anisotropic effects in topological quantum critical phenomena.