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Many-Body Spectral Functions from Steady State Density Functional Theory.

David Jacob1,2, Stefan Kurth1,2,3

  • 1Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Departamento de Física de Materiales , Universidad del País Vasco UPV/EHU , Avenida Tolosa 72 , E-20018 San Sebastián , Spain.

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Summary

We present a method to determine the many-body spectral function of interacting electrons using equilibrium density functional theory (DFT). This approach utilizes an ideal scanning tunneling microscope (STM) setup and steady-state DFT (i-DFT) for accurate calculations.

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Anderson modelDensity functional theoryexchange-correlation biasmany-body spectral functionsteady state transport

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Area of Science:

  • Condensed Matter Physics
  • Quantum Chemistry
  • Materials Science

Background:

  • Extracting many-body spectral functions is crucial for understanding electron interactions in materials.
  • Traditional methods often struggle with accuracy for complex interacting systems.
  • Density Functional Theory (DFT) provides a computationally feasible framework, but extensions are needed for many-body effects.

Purpose of the Study:

  • To develop a scheme for calculating the exact equilibrium many-body spectral function from equilibrium DFT.
  • To establish a connection between interacting spectral functions and Kohn-Sham spectral functions within a novel formalism.
  • To validate the proposed method on nontrivial model systems.

Main Methods:

  • Devising an ideal scanning tunneling microscope (STM) setup with a weakly coupled probe.
  • Employing the steady-state DFT (i-DFT) formalism to calculate steady current.
  • Analyzing the normalized differential conductance in the vanishing coupling limit.
  • Deriving an exact relation between the interacting and Kohn-Sham spectral functions.

Main Results:

  • The normalized differential conductance in the ideal STM limit precisely yields the equilibrium many-body spectral function.
  • An exact formula is derived, expressing the interacting spectral function via the Kohn-Sham one.
  • The scheme is successfully applied to the single Anderson impurity model and the Constant Interaction Model.

Conclusions:

  • The proposed scheme offers a pathway to accurately compute many-body spectral functions from equilibrium DFT.
  • This work bridges the gap between ab initio calculations and the detailed electronic properties of interacting systems.
  • The developed method has potential applications in various fields of condensed matter physics and materials science.