Related papers: Nevanlinna Analytic Continuation for Migdal-Eliash…
Simulations of finite temperature quantum systems provide imaginary frequency Green's functions that correspond one-to-one to experimentally measurable real-frequency spectral functions. However, due to the bad conditioning of the…
Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can…
Migdal-Eliashberg theory describes the properties of the normal and superconducting states of electron-phonon mediated superconductors based on a perturbative treatment of the electron-phonon interactions. It is necessary to include both…
Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multi-orbital systems, these quantities are related to positive semidefinite matrix-valued functions of the…
The single particle Green's function provides valuable information on the momentum and energy-resolved spectral properties for a strongly correlated system. In large-scale numerical calculations using quantum Monte Carlo (QMC), dynamical…
We investigate the applicability of Migdal--Eliashberg (ME) theory by revisiting Migdal's analysis within the dynamical mean-field theory framework. First, we compute spectral functions, the quasi-particle weight, the self energy,…
In this paper, we propose a new analytic continuation method to extract real frequency spectral functions from imaginary frequency Green's functions of quantum many-body systems. This method is based on the pole representation of Matsubara…
The ill-posed analytic continuation problem for Green's functions and self-energies is investigated by revisiting the Pad\'{e} approximants technique. We propose to remedy the well-known problems of the Pad\'{e} approximants by performing…
Analytic continuation aims to reconstruct real-time spectral functions from imaginary-time Green's functions; however, this process is notoriously ill-posed and challenging to solve. We propose a novel neural network architecture, named the…
Experimentally relevant signatures of superconductivity require access to real-frequency quantities, such as the spectral functions, optical response, and transport properties, yet Migdal-Eliashberg calculations are commonly performed on…
Information about the pairing mechanism for superconductivity is contained in the spectral weight for the anomalous (Gorkov) Green function. In the most general case, this spectral weight can change sign on the positive real axis or even be…
We reassess the validity of Migdal-Eliashberg (ME) theory for coupled electron-phonon systems for large couplings $\lambda$. Although model calculations have found that ME theory breaks down for $\lambda\sim 0.5$, it is routinely applied…
We present a new charge self-consistent scheme combining Density Functional and Dynamical Mean Field Theory, which uses Green's function of multiple scattering-type. In this implementation the many-body effects are incorporated into the…
Analytic continuation is a critical step in quantum many-body computations, connecting imaginary-time or Matsubara Green's functions with real-frequency spectral functions, which can be directly compared to experimental results. However,…
The electromagnetic Green's function is expressed from the inverse Helmholtz operator, where a second frequency has been introduced as a new degree of freedom. The first frequency results from the frequency decomposition of the…
We formulate an efficient scheme to perform Migdal-Eliashberg calculation considering the retardation effect from first principles. While the conventional approach requires a huge number of Matsubara frequencies, we show that the…
The ill-posed analytic continuation problem for Green's functions or self-energies can be done using the Pad\'e rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of…
The purpose of analytical continuation is to establish a real frequency spectral representation of single-particle or two-particle correlation function (such as Green's function, self-energy function, and dynamical susceptibilities) from…
Green's functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along…
Theory of superconductivity in two-band non-adiabatic systems with strong electron correlations in the linear approximation over non-adiabaticity is built in the article. Having assumed weak electron-phonon interaction analytical…