Sturm spectral representations of Green's functions in the theory of many-fermion systems

Donald H. Kobe

Wei H

Using Schrodinger wave function in quantum field theory, the time-dependent Green func-tion and its spectral representation for 2-fermion system are derived, and the Schrodinger equa-tion as well as the normalization condition of his wave function are deduced. The normali-zation condition shows that this wave function i just the probability amplitude when energy-dependence of potential can be neglected. The Green functions for some other equal-time equa-tions are evaluated, however, the normalization of these equations remains to be solved and thepotential is non-Hermitian.

Donald H. Kobe

Lizeth Fernanda Silva Godoy, Jorge Milton Lara Sinaluisa, Cristian Luis Inca Balseca +3 more

In this article, the numerical level representation of imaginary time Green's functions based on a low rank decomposition of the discrete Lehmann spectral representation (DLR) using an effective spectral density has been presented with illustrative efficiency. The DLR basis consists of a collection of exponentials chosen by interpolation decomposition to ensure stable and efficient recovery of imaginary time Green functions or Matsubara frequency samples (Kaye et al., 2022). This implementation to fit behavior of a low-temperature spinless free fermionics-electron gas quantum system requires much fewer degrees of freedom for the standard discretizations. The basic functions of DLR are explicit; carefully chosen to ensure a stable and accurate approach, simplifying standard operations. Importantly, the function can be explicitly transformed to the Matsubara frequency domain or obtained directly by interpolation on a Matsubara frequency grid.

Majid Modarres, Younes Younesizadeh