Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions DOI Creative Commons
Selina Dirnböck, Seung‐Sup B. Lee, Fabian B. Kugler

et al.

Physical Review Research, Journal Year: 2024, Volume and Issue: 6(4)

Published: Dec. 2, 2024

Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size discontinuity structure, they challenging handle numerically. Recently, two advances were made tackle this problem: first, the overcomplete intermediate representation (OIR), which provides highly efficient compression Green's in imaginary frequency, second, partial spectral (PSFs), allow for an evaluation real frequency. We show that there is two-to-one correspondence between PSFs OIR coefficients exploit fact construct three-or-more-particle propagators. then use fit compress imaginary-frequency data obtained from numerical renormalization group (NRG), reaching ratio more than 400. Finally, we attempt match NRG. Due overcompleteness, achieve only qualitative agreement. Published by American Physical Society 2024

Language: Английский

General Shiba mapping for on-site four-point correlation functions DOI Creative Commons

Herbert Eßl,

M. Reitner, Giorgio Sangiovanni

et al.

Physical Review Research, Journal Year: 2024, Volume and Issue: 6(3)

Published: July 15, 2024

By applying the Shiba mapping on two-particle level, we derive relation between local four-point correlation functions of bipartite lattice models with on-site electronic repulsion and those corresponding attractive interaction in most general setting. In particular, extend results [], which were limited to rather specific situation static limit strictly particle-hole symmetric models, (i) by explicitly including magnetic field different values chemical potentials, (ii) considering full dependence generalized susceptibilities transfer (bosonic) Matsubara frequency. The derived formalism is then applied, as a relevant benchmark, Hubbard atom investigating properties divergences its irreducible vertex function potential applied field. resulting phase diagrams provide an insightful compass for future studies breakdown self-consistent perturbation expansion beyond high-symmetric regimes. Published American Physical Society 2024

Language: Английский

Citations

3
Feynman diagrammatics based on discrete pole representations: A path to renormalized perturbation theories DOI

Daria Gazizova,

L. Zhang, Emanuel Gull

et al.

Physical review. B./Physical review. B, Journal Year: 2024, Volume and Issue: 110(7)

Published: Aug. 27, 2024

By merging algorithmic Matsubara integration with discrete pole representations we present a procedure to generate fully analytic closed form results for impurity problems at fixed perturbation order. To demonstrate the utility of this approach study Bethe lattice and evaluate second-order self-energy which reliable benchmarks exist. We show that, when evaluating diagrams on axis, sums are extremely precise. point out absence numerical sign problem in evaluation, explore application same real-frequency evaluation diagrams. find that subject noise is controlled low temperatures can be mitigated additional computational expense. further by dynamical mean field bold diagrammatic self-consistency schemes both second fourth order compare where available.

Language: Английский

Citations

2
KeldyshQFT: A C++ codebase for real-frequency multiloop functional renormalization group and parquet computations of the single-impurity Anderson model DOI Creative Commons
Nepomuk Ritz,

Anxiang Ge,

Elias Walter

et al.

The Journal of Chemical Physics, Journal Year: 2024, Volume and Issue: 161(5)

Published: Aug. 7, 2024

We provide a detailed exposition of our computational framework designed for the accurate calculation real-frequency dynamical correlation functions single-impurity Anderson model in regime weak to intermediate coupling. Using quantum field theory within Keldysh formalism directly access self-energy and susceptibilities real frequencies, as recent publication [Ge et al., Phys. Rev. B 109, 115128 (2024)], primary challenge is full three-dimensional dependence four-point vertex. Our codebase provides fully MPI+OpenMP parallelized implementation functional renormalization group (fRG) self-consistent parquet equations approximation. It leverages vectorization handle additional complexity imposed by formalism, using optimized data structures highly performant integration routines. Going beyond results shown previous publication, code includes functionality perform fRG calculations multiloop framework, up arbitrary loop order, including iterations. Moreover, implementations various regulators, such hybridization, interaction, frequency, temperature, are supplied.

Language: Английский

Citations

1
Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions DOI Creative Commons
Selina Dirnböck, Seung‐Sup B. Lee, Fabian B. Kugler

et al.

Physical Review Research, Journal Year: 2024, Volume and Issue: 6(4)

Published: Dec. 2, 2024

Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size discontinuity structure, they challenging handle numerically. Recently, two advances were made tackle this problem: first, the overcomplete intermediate representation (OIR), which provides highly efficient compression Green's in imaginary frequency, second, partial spectral (PSFs), allow for an evaluation real frequency. We show that there is two-to-one correspondence between PSFs OIR coefficients exploit fact construct three-or-more-particle propagators. then use fit compress imaginary-frequency data obtained from numerical renormalization group (NRG), reaching ratio more than 400. Finally, we attempt match NRG. Due overcompleteness, achieve only qualitative agreement. Published by American Physical Society 2024

Language: Английский

Citations

1