Real-frequency quantum field theory applied to the single-impurity Anderson model DOI Creative Commons

Anxiang Ge,

Nepomuk Ritz, Elias Walter

et al.

arXiv (Cornell University), Journal Year: 2023, Volume and Issue: unknown

Published: Jan. 1, 2023

A major challenge in the field of correlated electrons is computation dynamical correlation functions. For comparisons with experiment, one interested their real-frequency dependence. This difficult to compute, as imaginary-frequency data from Matsubara formalism require analytic continuation, a numerically ill-posed problem. Here, we apply quantum theory single-impurity Anderson model (AM), using Keldysh instead direct access self-energy and susceptibilities on axis. We present results functional renormalization group (fRG) at one-loop level solving self-consistent parquet equations approximation. In contrast previous fRG works, employ parametrization four-point vertex which captures its full dependence three arguments. compare our benchmark obtained numerical second-order perturbation theory. find that capturing frequency significantly improves compared implementations, yields best agreement NRG data, but only feasible up moderate interaction strengths. Our methodical advances pave way for treating more complicated models future.

Language: Английский

Compactness of quantics tensor train representations of local imaginary-time propagators DOI Creative Commons

Haruto Takahashi,

Rihito Sakurai, Hiroshi Shinaoka

et al.

SciPost Physics, Journal Year: 2025, Volume and Issue: 18(1)

Published: Jan. 8, 2025

Space-time dependence of imaginary-time propagators, vital for ab initio and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X 13, 021015 (2023)]. However, the impact system parameters, like temperature, data size remains underexplored. This paper provides a comprehensive numerical analysis compactness local propagators in QTT one-time/-frequency objects two-time/-frequency objects, considering truncation terms Frobenius maximum norms. To study worst-case scenarios, we employ random pole models, where number poles grows logarithmically with inverse temperature coefficients are random. The Green’s functions generated by these models expected more difficult compress than those from physical systems. reveals that highly QTT, outperforming state-of-the-art approaches such as intermediate representation discrete Lehmann reprensentation. For bond dimensions saturate at low temperatures, especially norm. We provide counting-number arguments saturation while origin this clarified. paper’s findings highlight critical need further research selection methods, tolerance levels, choice between imaginary-frequency representations practical applications.

Language: Английский

Citations

2
Analytic Continuation of Multipoint Correlation Functions DOI Creative Commons

Anxiang Ge,

Johannes Halbinger, Seung‐Sup B. Lee

et al.

Annalen der Physik, Journal Year: 2024, Volume and Issue: 536(7)

Published: May 1, 2024

Abstract Conceptually, the Matsubara formalism (MF), using imaginary frequencies, and Keldysh (KF), formulated in real give equivalent results for systems thermal equilibrium. The MF has less complexity is thus more convenient than KF. However, computing dynamical observables requires analytic continuation from to frequencies. well‐known two‐point correlation functions (having one frequency argument), but, multipoint correlators, a straightforward recipe deducing all components correlator had not been yet. Recently, representation of KF correlators terms formalism‐independent partial spectral formalism‐specific kernels was introduced by Kugler, Lee, von Delft [Phys. Rev. X 11, 041006 (2021)]. This used formally elucidate connection between both formalisms. How can be analytically continued recover yield its counterpart shown. procedure illustrated various Hubbard atom.

Language: Английский

Citations

4
Subleading logarithmic behavior in the parquet formalism DOI Creative Commons
Marcel Gievers, Richard Schmidt, Jan von Delft

et al.

Physical review. B./Physical review. B, Journal Year: 2025, Volume and Issue: 111(8)

Published: Feb. 27, 2025

The Fermi-edge singularity in x-ray absorption spectra of metals is a paradigmatic case logarithmically divergent perturbation series. Prior work has thoroughly analyzed the leading logarithmic terms. Here, we investigate theory beyond logarithms and formulate self-consistent equations to incorporate all next-to-leading This parquet solution goes previous first-order sheds new light on formalism regarding behavior. We present numerical results Matsubara discuss characteristic power laws. also show that, within single-boson exchange framework, multi-boson diagrams are needed already at level. Published by American Physical Society 2025

Language: Английский

Citations

0
Dynamical Scaling and Planckian Dissipation Due to Heavy-Fermion Quantum Criticality DOI Creative Commons
Andreas Gleis, Seung‐Sup B. Lee, Gabriel Kotliar

et al.

Physical Review Letters, Journal Year: 2025, Volume and Issue: 134(10)

Published: March 10, 2025

We study dynamical scaling associated with a Kondo-breakdown quantum-critical point (KB QCP) of the periodic Anderson model, treated by two-site cellular mean-field theory (2CDMFT). In region, staggered-spin susceptibility exhibits ω/T scaling. propose ansatz that describes this behavior and reveals Planckian dissipation for longest-lived excitations. The current follows same scaling, leading to strange-metal optical conductivity resistivity. Importantly, is driven strong short-ranged vertex contributions, not single-particle decay. This suggests KB QCP described 2CDMFT novel (i.e., disorder-free) fixed point. Our results match experimental observations on YbRh2Si2 CeCoIn5. Published American Physical Society 2025

Language: Английский

Citations

0
Two-particle calculations with quantics tensor trains: Solving the parquet equations DOI Creative Commons
Stefan Rohshap, Marc K. Ritter, Hiroshi Shinaoka

et al.

Physical Review Research, Journal Year: 2025, Volume and Issue: 7(2)

Published: April 24, 2025

We present an application of quantics tensor trains (QTTs) and cross interpolation (TCI) to the solution a full set self-consistent equations for multivariate functions, so-called parquet equations. show that steps needed evaluate (Bethe-Salpeter equations, equation, Schwinger-Dyson equation) can be decomposed into basic operations on QTT-TCI compressed objects. The repeated these does not lead loss accuracy beyond specified tolerance iterative scheme converges even numerically demanding parameters. As examples, we take Hubbard model in atomic limit single impurity Anderson model, where objects two-particle vertices, depend three frequencies, but momenta. results this approach is able overcome major computational bottlenecks standard numerical methods. applied methods allow exponential increase number grid points included calculations, corresponding reduction error, linear cost. Published by American Physical Society 2025

Language: Английский

Citations

0
Real-frequency quantum field theory applied to the single-impurity Anderson model DOI Creative Commons

Anxiang Ge,

Nepomuk Ritz, Elias Walter

et al.

arXiv (Cornell University), Journal Year: 2023, Volume and Issue: unknown

Published: Jan. 1, 2023

A major challenge in the field of correlated electrons is computation dynamical correlation functions. For comparisons with experiment, one interested their real-frequency dependence. This difficult to compute, as imaginary-frequency data from Matsubara formalism require analytic continuation, a numerically ill-posed problem. Here, we apply quantum theory single-impurity Anderson model (AM), using Keldysh instead direct access self-energy and susceptibilities on axis. We present results functional renormalization group (fRG) at one-loop level solving self-consistent parquet equations approximation. In contrast previous fRG works, employ parametrization four-point vertex which captures its full dependence three arguments. compare our benchmark obtained numerical second-order perturbation theory. find that capturing frequency significantly improves compared implementations, yields best agreement NRG data, but only feasible up moderate interaction strengths. Our methodical advances pave way for treating more complicated models future.

Language: Английский

Citations

7