Stability and complexity of global iterative solvers for the Kadanoff-Baym equations

Gašperlin, Jože (avtor), Golež, Denis (avtor), Kaye, Jason (avtor)

Although the Kadanoff-Baym equations are typically solved using time-stepping methods, iterative global-in-time solvers offer potential algorithmic advantages, particularly when combined with compressed representations of two-time objects. We examine the computational complexity and stability of several global-in-time iterative methods, including multiple variants of fixed point iteration, Jacobian-free methods, and a Newton-Krylov method using automatic differentiation. We consider the ramped and periodically-driven Falicov-Kimball and Hubbard models within time-dependent dynamical mean-field theory. Although we observe that several iterative methods yield stable convergence at large propagation times, a standard forward fixed point iteration does not. We find that the number of iterations required to converge to a given accuracy with a fixed time step size scales roughly linearly with the number of time steps. This scaling is associated with the formation of a propagating front in the residual error, whose velocity is method-dependent. We identify key challenges which must be addressed in order to make global solvers competitive with time-stepping methods.

• Jezik: Angleški jezik
• Ključne besede: Anderson model, Green's functions, Mott insulators
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: 29 str.
• Številčenje: Vol. 21, iss. 3, art. no. 066
• PID: 20.500.12556/RUL-188108
• UDK: 538.9
• ISSN pri članku: 2542-4653
• DOI: 10.21468/SciPostPhys.21.3.066
• COBISS.SI-ID: 291565571
• Datum objave v RUL: 18.09.2026

Gradivo je del revije

• Naslov: SciPost physics
• Založnik: SciPost Foundation
• ISSN: 2542-4653
• COBISS.SI-ID: 526154521

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: Andersonov model, Greenove funkcije, Mottovi izolatorji