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Body-Ordered Approximations of Atomic Properties.

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Summary
This summary is machine-generated.

We demonstrate that the local density of states in tight-binding models exhibits a weak body-order expansion. This finding offers rapid convergence for electron density and energy calculations, aiding electronic structure problem-solving.

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Area of Science:

  • Condensed matter physics
  • Quantum chemistry
  • Materials science

Background:

  • Tight-binding models are fundamental for understanding electronic properties in solids.
  • Calculating electronic structure often involves approximations due to computational complexity.
  • The local density of states (LDOS) is a key quantity for characterizing electronic behavior.

Purpose of the Study:

  • To investigate the convergence properties of body-order expansions for LDOS in tight-binding models.
  • To establish the rate of convergence for analytic observables derived from LDOS.
  • To explore the implications for computational modeling in materials science.

Main Methods:

  • Analysis of tight-binding models.
  • Mathematical proof of body-order expansion convergence.
  • Investigation of analytic observables like electron density and energy.

Main Results:

  • Demonstration of a weak body-order expansion for LDOS in a broad class of tight-binding models.
  • Proof of exponential convergence for analytic observables (electron density, energy).
  • Convergence holds for both finite Fermi-temperature and zero-temperature insulators.

Conclusions:

  • The established exponential convergence provides a powerful tool for efficient electronic structure calculations.
  • Findings can significantly impact the modeling of potential energy landscapes.
  • This work offers a pathway to more accurate and computationally feasible solutions for complex electronic systems.