Spectral density reconstruction with Chebyshev polynomials

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.

14 pages, 6 figures

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Cited by in corpus (12)

• Quantum error mitigation for Fourier moment computation
• Demonstration of the Rodeo Algorithm on a Quantum Computer
• Faster spectral density calculation using energy moments
• Spectral features of polaronic excitations in a superconducting analog simulator
• Spectral function for ${}^4$He using the Chebyshev expansion in coupled-cluster theory
• Linear-scale simulations of quench dynamics
• Near-term quantum algorithm for computing molecular and materials properties based on recursive variational series methods
• Calculation of Dynamical Response Functions Using a Bound-state Method
• Inclusive quasielastic (anti-)neutrino nucleus scattering within the Standard Model and beyond
• Optimized binning for response function reconstruction via Chebyshev expansions
• Nuclear two point correlation functions on a quantum-computer
• Quantum Simulation of Nuclear Dynamics in First Quantization