Continuous-pole-expansion method to obtain spectra of electronic lattice models

Abstract

We present a new algorithm to analytically continue the self-energy of quantum many-body systems from Matsubara frequencies to the real axis. The method allows straightforward, unambiguous computation of electronic spectra for lattice models of strongly correlated systems from self-energy data that has been collected with state-of-the-art continuous time solvers within dynamical mean-field simulations. Using well-known analytical properties of the self-energy, the analytic continuation is cast into a constrained minimization problem that can be formulated as a quadratic programmable optimization with linear constraints. The algorithm is validated against exactly solvable finite-size problems, showing that all features of the spectral function near the Fermi level are very well reproduced and coarse features are reproduced for all energies. The method is applied to two well-known lattice problems, the two-dimensional Hubbard model at half filling, where the momentum dependence of the gap formation is studied, as well as a multiband model of NiO, for which the spectral function can be directly compared to experiment. Agreement with published results is very good.

DFT+DMFT calculations of the complex band and tunneling behavior for the transition metal monoxides MnO, FeO, CoO, and NiO

“…The four monoxides, especially NiO, have been extensively studied in the DMFT community and used as benchmark material for novel computational methods [17][18][19] . The existing DFT+DMFT calculations of NiO were not done in the exactly same way.…”

“…The number of Monte Carlo sweeps in the QMC calculation is 10 6 in each solver run. The continuous-pole-expansion method 19 is used for obtaining the self-energy and impurity Green's function in real frequency domain.…”

“…NiO has also been actively used as a benchmark material for DFT+DMFT method development, e.g. new methods related to the double counting correction 18,22,39 and analytical continuation 19 . The other members of the late TM monoxides, CoO, FeO and MnO, together with NiO have been studied within the DFT+DMFT scheme in a systematic investigation of the band gaps of these materials 22 , investigation of the fundamental quantum entanglement of in-distinguishable particles 40 , and as benchmarking materials in method developments for determining the Coulomb correlation strength 41,42 .…”

All-electron self-consistentGWin the Matsubara-time domain: Implementation and benchmarks of semiconductors and insulators

“…The reliability of this approximation remains under debate, and recently Staar and co-workers have proposed the continuous-pole expansion (CPE) as an alternative algorithm for analytic continuation from the Matsubara-frequency to the real-frequency domain. 40 Unlike the Pade approximation, this method explicitly takes into account the physical causality that places a constraint on the self-energy.…”

Characterizing featureless Mott insulating state by quasiparticle interference: A dynamical mean field theory view

“…In order to obtain the electron Green function in real frequency G b ( k, ω), a numerical calculation of the analytic continuation on Σ(iω n ) is necessary. We adopt the continuous-pole-expansion method 30 recently developed by Staar, et al to numerically perform the analytic continuation on Σ(iω n ). This method is shown to be an efficient approach to find an accurate and unambiguous result of the analytic continuation within a finite range of frequency, which is necessary for the current study.…”