Abstract

Correlated real-time dynamics in large, spatially inhomogeneous quantum systems remain difficult to access with nonequilibrium many-body methods. Existing large-scale approaches often rely on effective single-particle, static, or adiabatic descriptions, whereas two-time nonequilibrium Green functions retain dynamical correlations and memory but their computational runtime grows cubically with the number of time steps Nt. This scaling bottleneck could recently be overcome by introducing the G1–G₂ scheme [Schlǖnzen et al., Phys. Rev. Lett. 124, 076601 (2020)]—a time-local reformulation of the Generalized Kadanoff-Baym ansatz with Hartree-Fock propagators (HF-GKBA)—that is linear in Nt, but still requires the propagation of a two-particle correlation function and may suffer from numerical instabilities. This has restricted time-dependent dynamical NEGF simulations to small systems with Nb ∼102 basis states. Here we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted δNEGF, that represents dynamical two-particle correlations through fluctuations of field-operator products, δ Ĝ. This factorized representation guarantees stable dynamics by preserving the positivity of the reduced density matrices, avoids the explicit storage of the two-particle Green function, and reduces the propagation to a finite ensemble of Hartree-Fock-like fluctuation trajectories that can be evolved independently and in parallel. Combined with a stochastic low-rank decomposition of the correlation functions, the method retains time-linear scaling while extending dynamical GW and particle-particle and particle-hole T-matrix simulations to basis sizes of order Nb ∼104, roughly two orders of magnitude beyond previous time-dependent dynamical NEGF calculations. We benchmark δNEGF against exact and HF-GKBA results for lattice systems, finding stable correlated dynamics also at strong coupling. We further demonstrate large-scale simulations of diffusion in two-dimensional Hubbard lattices and, as an outlook beyond local Hubbard interactions, ultrafast relaxation in graphene nanoribbon heterostructures with long-range Coulomb interactions. These results establish δNEGF as a scalable route to dynamical self-energy simulations of large, spatially inhomogeneous correlated quantum systems beyond the reach of existing NEGF implementations.

Abstract

Correlated real-time dynamics in large, spatially inhomogeneous quantum systems remain difficult to access with nonequilibrium many-body methods. Existing large-scale approaches often rely on effective single-particle, static, or adiabatic descriptions, whereas two-time nonequilibrium Green functions retain dynamical correlations and memory but their computational runtime grows cubically with the number of time steps Nt. This scaling bottleneck could recently be overcome by introducing the G1–G₂ scheme [Schlǖnzen et al., Phys. Rev. Lett. 124, 076601 (2020)]—a time-local reformulation of the Generalized Kadanoff-Baym ansatz with Hartree-Fock propagators (HF-GKBA)—that is linear in Nt, but still requires the propagation of a two-particle correlation function and may suffer from numerical instabilities. This has restricted time-dependent dynamical NEGF simulations to small systems with Nb ∼102 basis states. Here we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted δNEGF, that represents dynamical two-particle correlations through fluctuations of field-operator products, δ Ĝ. This factorized representation guarantees stable dynamics by preserving the positivity of the reduced density matrices, avoids the explicit storage of the two-particle Green function, and reduces the propagation to a finite ensemble of Hartree-Fock-like fluctuation trajectories that can be evolved independently and in parallel. Combined with a stochastic low-rank decomposition of the correlation functions, the method retains time-linear scaling while extending dynamical GW and particle-particle and particle-hole T-matrix simulations to basis sizes of order Nb ∼104, roughly two orders of magnitude beyond previous time-dependent dynamical NEGF calculations. We benchmark δNEGF against exact and HF-GKBA results for lattice systems, finding stable correlated dynamics also at strong coupling. We further demonstrate large-scale simulations of diffusion in two-dimensional Hubbard lattices and, as an outlook beyond local Hubbard interactions, ultrafast relaxation in graphene nanoribbon heterostructures with long-range Coulomb interactions. These results establish δNEGF as a scalable route to dynamical self-energy simulations of large, spatially inhomogeneous correlated quantum systems beyond the reach of existing NEGF implementations.

Abstract

Correlated real-time dynamics in large, spatially inhomogeneous quantum systems remain difficult to access with nonequilibrium many-body methods. Existing large-scale approaches often rely on effective single-particle, static, or adiabatic descriptions, whereas two-time nonequilibrium Green functions retain dynamical correlations and memory but their computational runtime grows cubically with the number of time steps Nt. This scaling bottleneck could recently be overcome by introducing the G1–G₂ scheme [Schlǖnzen et al., Phys. Rev. Lett. 124, 076601 (2020)]—a time-local reformulation of the Generalized Kadanoff-Baym ansatz with Hartree-Fock propagators (HF-GKBA)—that is linear in Nt, but still requires the propagation of a two-particle correlation function and may suffer from numerical instabilities. This has restricted time-dependent dynamical NEGF simulations to small systems with Nb ∼102 basis states. Here we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted δNEGF, that represents dynamical two-particle correlations through fluctuations of field-operator products, δ Ĝ. This factorized representation guarantees stable dynamics by preserving the positivity of the reduced density matrices, avoids the explicit storage of the two-particle Green function, and reduces the propagation to a finite ensemble of Hartree-Fock-like fluctuation trajectories that can be evolved independently and in parallel. Combined with a stochastic low-rank decomposition of the correlation functions, the method retains time-linear scaling while extending dynamical GW and particle-particle and particle-hole T-matrix simulations to basis sizes of order Nb ∼104, roughly two orders of magnitude beyond previous time-dependent dynamical NEGF calculations. We benchmark δNEGF against exact and HF-GKBA results for lattice systems, finding stable correlated dynamics also at strong coupling. We further demonstrate large-scale simulations of diffusion in two-dimensional Hubbard lattices and, as an outlook beyond local Hubbard interactions, ultrafast relaxation in graphene nanoribbon heterostructures with long-range Coulomb interactions. These results establish δNEGF as a scalable route to dynamical self-energy simulations of large, spatially inhomogeneous correlated quantum systems beyond the reach of existing NEGF implementations.

Abstract

Correlated real-time dynamics in large, spatially inhomogeneous quantum systems remain difficult to access with nonequilibrium many-body methods. Existing large-scale approaches often rely on effective single-particle, static, or adiabatic descriptions, whereas two-time nonequilibrium Green functions retain dynamical correlations and memory but their computational runtime grows cubically with the number of time steps Nt. This scaling bottleneck could recently be overcome by introducing the G1–G₂ scheme [Schlǖnzen et al., Phys. Rev. Lett. 124, 076601 (2020)]—a time-local reformulation of the Generalized Kadanoff-Baym ansatz with Hartree-Fock propagators (HF-GKBA)—that is linear in Nt, but still requires the propagation of a two-particle correlation function and may suffer from numerical instabilities. This has restricted time-dependent dynamical NEGF simulations to small systems with Nb ∼102 basis states. Here we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted δNEGF, that represents dynamical two-particle correlations through fluctuations of field-operator products, δ Ĝ. This factorized representation guarantees stable dynamics by preserving the positivity of the reduced density matrices, avoids the explicit storage of the two-particle Green function, and reduces the propagation to a finite ensemble of Hartree-Fock-like fluctuation trajectories that can be evolved independently and in parallel. Combined with a stochastic low-rank decomposition of the correlation functions, the method retains time-linear scaling while extending dynamical GW and particle-particle and particle-hole T-matrix simulations to basis sizes of order Nb ∼104, roughly two orders of magnitude beyond previous time-dependent dynamical NEGF calculations. We benchmark δNEGF against exact and HF-GKBA results for lattice systems, finding stable correlated dynamics also at strong coupling. We further demonstrate large-scale simulations of diffusion in two-dimensional Hubbard lattices and, as an outlook beyond local Hubbard interactions, ultrafast relaxation in graphene nanoribbon heterostructures with long-range Coulomb interactions. These results establish δNEGF as a scalable route to dynamical self-energy simulations of large, spatially inhomogeneous correlated quantum systems beyond the reach of existing NEGF implementations.