Fourier transformation and response functions

Abstract

We improve on Fourier transforms (FT) between imaginary time $\tau$ and imaginary frequency ${\omega }_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Green's function can be improved by using a "sumrule" boundary condition for a spline. For response functions a two-dimensional FT of a singular function is required. We show how this can be done efficiently by splitting off a one-dimensional part containing the singularity and by performing a semi-analytical FT for the remaining more innocent two-dimensional part.

4 pages, 3 figures

References in corpus (9)

• 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
• Dual Fermion Approach to Susceptibility of Correlated Lattice Fermions
• A weak coupling CTQMC study of the single impurity and periodic Anderson models with s-wave superconducting baths
• Dynamical vertex approximation for nanoscopic systems
• The anharmonic electron-phonon problem

Cited by in corpus (6)

• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Efficient treatment of two-particle vertices in dynamical mean-field theory
• Parquet decomposition calculations of the electronic self-energy
• An Improvement in Quantum Fourier Transform