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Localizing Transitions via Interaction-Induced Flat Bands.

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This study introduces a new theory for interaction-induced band flattening in correlated electron systems. It reveals a generic mechanism for creating flat bands, crucial for understanding spontaneous symmetry breaking in materials.

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Area of Science:

  • Condensed Matter Physics
  • Theoretical Physics
  • Quantum Mechanics

Background:

  • Strongly correlated electron systems exhibit complex phenomena.
  • Flat bands in electronic systems are linked to unique quantum properties.
  • Topological concepts offer novel ways to engineer material properties.

Purpose of the Study:

  • To develop a theoretical framework for interaction-induced band flattening.
  • To establish a generic method for constructing flat bands using topological zero modes.
  • To explore the role of such mechanisms in spontaneous symmetry breaking.

Main Methods:

  • Developing a theory connecting flat bands with index theorems.
  • Constructing flat bands via periodic repetition of local Hamiltonians with topological zero modes.
  • Analyzing interacting models of Dirac fermions in inhomogeneous fields using Hubbard-Stratonovich transformations.

Main Results:

  • Demonstrated a method to create perfectly flat bands for Dirac particles in periodic magnetic fields.
  • Derived exact analytical solutions for flat band wave functions.
  • Showed that specific field configurations induce band flattening in interacting Dirac fermions, energetically favoring localization in systems with nearly flat bands.

Conclusions:

  • Interaction-induced band flattening is a generic nonperturbative mechanism for spontaneous symmetry breaking.
  • This mechanism is relevant to various strongly correlated electron systems.
  • Superconductivity and other symmetry-breaking channels are potential avenues for realizing these effects.