Chebyshev polynomial representation of imaginary-time response functions

Problems of finite-temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) -time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian (as compared to temperature) necessitates a very precis...

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Bibliographic Details
Published in:Physical review. B 2018-08, Vol.98 (7), p.075127
Main Authors: Gull, Emanuel, Iskakov, Sergei, Krivenko, Igor, Rusakov, Alexander A, Zgid, Dominika
Format: Article
Language:English
Subjects:
Chebyshev approximation
Fourier transforms
Green's functions
Hamiltonian functions
Mathematical analysis
Polynomials
Quantum statistics
Representations
Response functions
Series expansion
Statistical mechanics
Thermal expansion
Time response
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Summary:Problems of finite-temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) -time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian (as compared to temperature) necessitates a very precise representation of these functions. In this paper, we explore the representation of Green's functions and self-energies in terms of a series of Chebyshev polynomials. We show that many operations, including convolutions, Fourier transforms, and the solution of the Dyson equation, can straightforwardly be expressed in terms of the series expansion coefficients. We then compare the accuracy of the Chebyshev representation for realistic systems with the uniform-power grid representation, which is most commonly used in this context.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.98.075127