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Spectral density reconstruction with Chebyshev polynomials.

Joanna E Sobczyk1, Alessandro Roggero2,3,4

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Summary
This summary is machine-generated.

This study introduces a quantum algorithm to accurately calculate spectral density in quantum many-body systems. It overcomes numerical inversion issues, enabling precise analysis for nuclear physics and condensed matter applications.

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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Physics
  • Nuclear Physics

Background:

  • Accurate spectral density calculations are crucial for understanding quantum many-body systems in linear response.
  • Integral transform techniques are vital but limited by ill-conditioned numerical inversion.
  • Applications include scattering cross sections in atomic nuclei and transport properties of nuclear/neutron star matter.

Purpose of the Study:

  • To extend a quantum algorithm for circumventing numerical inversion limitations in spectral density calculations.
  • To enable controllable reconstructions of spectral density with rigorous error estimates.
  • To demonstrate a proof-of-principle application in condensed matter physics.

Main Methods:

  • Extension of a novel quantum algorithm for spectral density reconstruction.
  • Development of controllable reconstruction methods with finite energy resolution and error bounds.
  • Utilizing Chebyshev polynomial expansions for efficient classical simulations.

Main Results:

  • Successfully circumvented the ill-conditioned numerical inversion problem.
  • Achieved controllable spectral density reconstructions with rigorous error estimates.
  • Demonstrated the method's efficacy by calculating the local density of states for graphene in a magnetic field.

Conclusions:

  • The extended quantum algorithm provides a robust method for accurate spectral density calculations.
  • This approach overcomes limitations of traditional integral transform techniques.
  • Paves the way for advanced applications in nuclear and condensed matter physics.