Spectral density reconstruction with Chebyshev polynomials
- URL: http://arxiv.org/abs/2110.02108v1
- Date: Tue, 5 Oct 2021 15:16:13 GMT
- Title: Spectral density reconstruction with Chebyshev polynomials
- Authors: Joanna E. Sobczyk, Alessandro Roggero
- Abstract summary: We show how to perform controllable reconstructions of a finite energy resolution with rigorous error estimates.
This paves the way for future applications in nuclear and condensed matter physics.
- Score: 77.34726150561087
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Accurate calculations of the spectral density in a strongly correlated
quantum many-body system are of fundamental importance to study its dynamics in
the linear response regime. Typical examples are the calculation of inclusive
and semi-exclusive scattering cross sections in atomic nuclei and transport
properties of nuclear and neutron star matter. Integral transform techniques
play an important role in accessing the spectral density in a variety of
nuclear systems. However, their accuracy is in practice limited by the need to
perform a numerical inversion which is often ill-conditioned. In the present
work we extend a recently proposed quantum algorithm which circumvents this
problem. We show how to perform controllable reconstructions of the spectral
density over a finite energy resolution with rigorous error estimates. An
appropriate expansion in Chebyshev polynomials allows for efficient simulations
also on classical computers. We apply our idea to reconstruct a simple model --
response function as a proof of principle. This paves the way for future
applications in nuclear and condensed matter physics.
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