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This study introduces a novel method to calculate Peierls phases in quantum systems using gauge-invariant magnetic flux, simplifying calculations for non-uniform fields. The approach accurately models phenomena like the Quantum Hall Effect and domain wall behavior in topological insulators.

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Area of Science:

  • Quantum Physics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Introducing magnetic fields into discrete quantum models typically uses the Peierls substitution, relying on magnetic vector potentials.
  • The non-uniqueness of the magnetic vector potential and gauge choice complicates calculations, especially for non-uniform fields.
  • Existing methods face challenges in efficiently determining Peierls phases for complex magnetic field configurations.

Purpose of the Study:

  • To develop a method for calculating Peierls phases directly from gauge-invariant magnetic flux, bypassing the need for vector potentials.
  • To simplify the analysis of quantum systems subjected to non-uniform magnetic fields.
  • To provide a computationally efficient and geometrically flexible approach for modeling quantum phenomena.

Main Methods:

  • Calculating Peierls phases directly from gauge-invariant magnetic flux, avoiding magnetic vector potential determination.
  • Employing a graphic algorithm, similar to 'dots and boxes', for phase assignment.
  • Implementing the method to model the Aharonov-Bohm effect, the Half-Integer Quantum Hall Effect in graphene, and multi-domain Chern insulators.

Main Results:

  • The proposed method successfully calculates Peierls phases without explicit gauge fixing.
  • The method reproduces the Half-Integer Quantum Hall Effect in graphene using an alternative phase assignment to the Landau gauge.
  • Simulations of multi-domain Chern insulators with decoherence and finite temperature show quantized resistances consistent with experimental results.

Conclusions:

  • The gauge-invariant flux method offers a robust alternative for calculating Peierls phases in discrete quantum models.
  • This approach simplifies the study of quantum systems with complex or non-uniform magnetic fields.
  • The findings have implications for understanding and modeling topological insulators and quantum Hall effects.