2018/05/31 by Emanuel Gull, Sergei Iskakov, Igor Krivenko +2 · 51 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Approximation theory #Chebyshev equation #Chebyshev filter #Chebyshev polynomials #Classical orthogonal polynomials #Context (archaeology) #Fourier series #Fourier transform #Hamiltonian (control theory) #Imaginary time #Mathematical analysis #Mathematical optimization #Mathematics #Orthogonal polynomials #Physics #Polynomial #Power series #Quantum #Quantum mechanics #Quantum statistical mechanics #Quantum, superfluid, helium dynamics #Representation (politics) #Spectroscopy and Quantum Chemical Studies #Supersymmetric quantum mechanics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.98.075127
published in Physical review. B./Physical review. B 98(7) (American Physical Society) · 11 pages, 8 figures
arxiv created 2018/08/15 · openalex publication_date 2018/08/15 · arxiv updated 2018/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.