Chebyshev polynomial representation of imaginary time response functions

Abstract

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.

arXiv comment11 pages, 8 figures

References in corpus (21)

• Continuous-time Monte Carlo methods for quantum impurity models
• Quantum Cluster Theories
• A continuous-time solver for quantum impurity models
• Continuous Time Quantum Monte Carlo method for fermions
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Continuous-time auxiliary field Monte Carlo for quantum impurity models
• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• The Band-Gap Problem in Semiconductors Revisited: Effects of Core States and Many-Body Self-Consistency
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Levels of self-consistency in the GW approximation
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• The description of strong correlation within self-consistent Green's function second-order perturbation theory
• Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data
• Second-order Green's function perturbation theory for periodic systems
• Efficient temperature-dependent Green's functions methods for realistic systems: compact grids for orthogonal polynomial transforms
• Exploring connections between statistical mechanics and Green's functions for realistic systems. Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green's function
• Efficient temperature-dependent Green's function methods for realistic systems: using cubic spline interpolation to approximate Matsubara Green's functions
• Fractional charge and spin errors in self-consistent Green's function theory
• Local Hamiltonians for quantitative Green's function embedding methods
• Performance analysis of a physically constructed orthogonal representation of imaginary-time Green's function
• Many-body Green's function theory for electron-phonon interactions: ground state properties of the Holstein dimer

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• irbasis: Open-source database and software for intermediate-representation basis functions of imaginary-time Green's function
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• Challenges with relativistic GW calculations in solids and molecules
• Interaction expansion inchworm Monte Carlo solver for lattice and impurity models
• Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions
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• Low rank Green's function representations applied to dynamical mean-field theory
• Equivariant neural network for Green's functions of molecules and materials
• Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals
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• cppdlr: Imaginary time calculations using the discrete Lehmann representation
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• Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm
• Precise Low-Temperature Expansions for the Sachdev-Ye-Kitaev model
• GW space-time method: Energy band-gap of solid hydrogen
• Nonpertubative Many-Body Theory for the Two-Dimensional Hubbard Model at Low Temperature: From Weak to Strong Coupling Regimes
• Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting