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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials Science

Background:

  • Computing topological invariants is challenging in systems lacking translational symmetry, like quasicrystals and supermoiré materials.
  • The large number of sites in these systems exceeds the capabilities of conventional computational methods.

Purpose of the Study:

  • To establish a scalable method for computing local topological invariants in exceptionally large two-dimensional quasicrystalline and supermoiré systems.
  • To enable the analysis of topological phases in systems with hundreds of millions of sites.

Main Methods:

  • Utilized tensor networks, specifically a Chebyshev tensor network algorithm, to represent the density matrix.
  • Developed a method for large-scale computation of topological markers in complex materials.

Main Results:

  • Successfully computed topological invariants for systems with up to hundreds of millions of sites, orders of magnitude larger than previously possible.
  • Demonstrated the methodology on two-dimensional quasicrystals with C8 and C10 rotational symmetries and Chern phase mosaics.

Conclusions:

  • The developed tensor network method provides a powerful tool for calculating topological phases in large-scale quasicrystalline and supermoiré systems.
  • This approach facilitates the theoretical understanding and rationalization of topological matter in these complex materials.