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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| Veröffentlicht in: | Physical review. B 2018-08, Vol.98 (7), p.075127 |
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| container_title | Physical review. B |
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| creator | Gull, Emanuel Iskakov, Sergei Krivenko, Igor Rusakov, Alexander A Zgid, Dominika |
| description | 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. |
| doi_str_mv | 10.1103/PhysRevB.98.075127 |
| format | Article |
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| language | eng |
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| source | American Physical Society |
| 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 |
| title | Chebyshev polynomial representation of imaginary-time response functions |
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