Accelerating nonequilibrium Green function simulations with embedding self-energies

Balzer, Karsten; Schlünzen, Niclas; Ohldag, Hannes; Joost, Jan‐Philip; Bönitz, M.

doi:10.1103/physrevb.107.155141

Cited by 4 publications

(3 citation statements)

References 45 publications

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“…This approximation was originally derived for equilibrium systems and in the weak scattering limit but has been found to work well also out of equilibrium [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Within the NEGF-GKBA and its recent reformulation as a time-linear scheme [25,26], it is currently possible to simulate the long-time dynamics of electronic systems with a basis size on the order of 100 orbitals [28].…”

Section: Generalized Kadanoff-baym Ansatzmentioning

confidence: 99%

“…Since we are interested in large systems with both fast and slow degrees of freedom, it is useful to make further approximations to reduce the time scaling. To this end, and inspired by other work on open systems [29,30,57,58], we introduce an AWBL based on an approximation to the collision integral (the right-hand side of Eq. 15).…”

Section: Approximate Wide-band Limitmentioning

confidence: 99%

“…Our method is an extension of the approach introduced in [15,16] and amounts to propagating the equation of motion for the electronic spin-dependent single-particle density matrix, together with the Landau-Lifshitz-Gilbert (LLG) equation for the classical spins. The former equation can be derived from the general theory of nonequilibrium Green's functions using the so-called generalized Kadanoff-Baym ansatz (GKBA) [17][18][19][20][21][22][23][24][25][26][27][28][29][30], and therefore allows to systematically introduce the effects of electron-electron interactions via diagrammatic manybody perturbation theory. In what follows, we apply this scheme to study current-induced skyrmion motion, fully accounting for the dynamics of the itinerant electrons resulting from an applied bias.…”

Section: Introductionmentioning

confidence: 99%

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Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures

Östberg,

Viñas Boström,

Verdozzi

2024

Front. Phys.

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Introduction: Magnetic skyrmions hold great promise for realizing compact and stable memory devices that can be manipulated at very low energy costs via electronic current densities.Methods: In this work, we extend a recently introduced method to describe classical skyrmion textures coupled to dynamical itinerant electrons. In this scheme, the electron dynamics is described via nonequilibrium Green’s function (NEGF) within the generalized Kadanoff–Baym ansatz, and the classical spins are treated via the Landau–Lifshitz–Gilbert equation. Here, the framework is extended to open systems by the introduction of a non-interacting approximation to the collision integral of NEGFs. This, in turn, allows us to perform computations of the real-time response of skyrmions to electronic currents in large quantum systems coupled to electronic reservoirs, which exhibit linear scaling in the number of time steps. We use this approach to investigate how electronic spin currents and dilute spin disorder affect skyrmion transport and the skyrmion Hall drift.Results: Our results show that the skyrmion dynamics is sensitive to a specific form of the spin disorder, such that different disorder configurations lead to qualitatively different skyrmion trajectories for the same applied bias.Discussion: This sensitivity arises from the local spin dynamics around the magnetic impurities, a feature that is expected not to be well-captured by phenomenological or spin-only descriptions. At the same time, our findings illustrate the potential of engineering microscopic impurity patterns to steer skyrmion trajectories.

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Section: Generalized Kadanoff-baym Ansatzmentioning

confidence: 99%

Section: Approximate Wide-band Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures

Östberg,

Viñas Boström,

Verdozzi

2024

Front. Phys.

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Two‐Time Quantum Fluctuations Approach and Its Relation to the Bethe–Salpeter Equation

Schroedter,

Bonitz

2024

Physica Status Solidi (b)

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Correlated quantum many‐particle systems out of equilibrium are of high interest in many fields, including correlated solids, ultracold atoms, or dense plasmas. Accurate theoretical description of these systems is challenging both, conceptionally and with respect to computational resources. A quantum fluctuations approach is recently presented, which is equivalent to the nonequilibrium GW approximation that promises high accuracy at low computational cost. The method exhibits process time scaling that is linear in the number of time steps, like the G1–G2 scheme, however, at a much reduced computer memory cost. In a second publication, this approach is extended to the two‐time exchange–correlation functions and the dynamic density response properties. Herein, the properties of this approach are analyzed in more detail. The physical meaning of the central approximation, the quantum polarization approximation, is established. It is demonstrated that the method is equivalent to the Bethe–Salpeter equation for the two‐time exchange–correlation function when the generalized Kadanoff–Baym ansatz with Hartree–Fock propagators is applied.

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Accelerating Nonequilibrium Green Functions Simulations: The G1–G2 Scheme and Beyond

Bonitz,

Joost,

Makait

et al. 2024

Physica Status Solidi (b)

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The theory of nonequilibrium Green functions (NEGF) has seen a rapid development over the recent three decades. Applications include diverse correlated many‐body systems in and out of equilibrium. Very good agreement with experiments and available exact theoretical results could be demonstrated if the proper selfenergy approximations were used. However, full two‐time NEGF simulations are computationally costly, as they suffer from a cubic scaling of the computation time with the simulation duration. Recently the G1–G2 scheme that exactly reformulates the generalized Kadanoff–Baym ansatz with Hartree–Fock propagators (HF‐GKBA) into time‐local equations is introduced, which achieves time‐linear scaling and allows for a dramatic speedup and extension of the simulations (Schluenzen et al. Phys. Rev. Lett. 2020, 124, 076601). Remarkably, this scaling is achieved quickly, and also for high‐level selfenergies, including the nonequilibrium GW and T‐matrix approximations (Joost et al. Phys. Rev. B 2020, 101, 245101). Even the dynamically screened ladder approximation is now feasible (Joost et al. Phys. Rev. B 2022, 105, 165155), and also applications to electron‐boson systems are demonstrated. Herein, an overview on recent results that are achieved with the G1–G2 scheme is presented. Problems and open questions are discussed and further ideas of how to overcome the current limitations of the scheme and present are presented. The G1–G2 scheme is illustrated by presenting applying it to the excitation dynamics of Hubbard clusters, to optical excitation of graphene, and to charge transfer during stopping of ions by correlated materials.

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Accelerating nonequilibrium Green function simulations with embedding self-energies

Cited by 4 publications

References 45 publications

Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures

Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures

Two‐Time Quantum Fluctuations Approach and Its Relation to the Bethe–Salpeter Equation

Accelerating Nonequilibrium Green Functions Simulations: The G1–G2 Scheme and Beyond

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