Correlated real-time dynamics in large, spatially inhomogeneous quantum systems remain difficult to access with nonequilibrium many-body methods. Two-time nonequilibrium Green functions (NEGF) retain dynamical correlations but their computational runtime grows cubically with the number of time steps $N_\mathrm{t}$ . This scaling bottleneck could recently be overcome by introducing the G1--G2 scheme that is linear in $N_\mathrm{t}$ , but requires propagation of a two-particle correlation function and may suffer from numerical instabilities. This has restricted simulations to small systems with $N_\mathrm{b} \sim 10^2$ basis states. Here we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted $δ$ NEGF, that represents dynamical two-particle correlations through fluctuations of field-operator products, $δ\hat G$ . This 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 trajectories. 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 $N_\mathrm{b}\sim 10^4$ . We benchmark $δ$ NEGF 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 ultrafast relaxation in graphene nanoribbon heterostructures with long-range Coulomb interactions. These results establish $δ$ NEGF as a scalable route to dynamical self-energy simulations of large, spatially inhomogeneous correlated quantum systems beyond the reach of existing NEGF implementations.Correlated real-time dynamics in large, spatially inhomogeneous quantum systems remain difficult to access with nonequilibrium many-body methods. Two-time nonequilibrium Green functions (NEGF) retain dynamical correlations but their computational runtime grows cubically with the number of time steps $N_\mathrm{t}$. This scaling bottleneck could recently be overcome by introducing the G1--G2 scheme that is linear in $N_\mathrm{t}$, but requires propagation of a two-particle correlation function and may suffer from numerical instabilities. This has restricted simulations to small systems with $N_\mathrm{b} \sim 10^2$ basis states. Here we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted $δ$NEGF, that represents dynamical two-particle correlations through fluctuations of field-operator products, $δ\hat G$. This 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 trajectories. 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 $N_\mathrm{b}\sim 10^4$. We benchmark $δ$NEGF 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 ultrafast relaxation in graphene nanoribbon heterostructures with long-range Coulomb interactions. These results establish $δ$NEGF as a scalable route to dynamical self-energy simulations of large, spatially inhomogeneous correlated quantum systems beyond the reach of existing NEGF implementations.

arXiv:2606.10773Jun 9, 20260 citations

Time-dependent quantum dynamics

SC Althorpe, Pavel Soldán, Gabriel G. Balint‐Kurti

Jan 1, 20014 citations

Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations

Niclas Schlünzen, Jan‐Philip Joost, M. Bönitz

The dynamics of strongly correlated fermions following an external excitation reveals extremely rich collective quantum effects. Examples are fermionic atoms in optical lattices, electrons in correlated materials, and dense quantum plasmas. Presently, the only quantum-dynamics approach that rigorously describes these processes in two and three dimensions is the nonequilibrium Green functions (NEGF) method. However, NEGF simulations are computationally expensive due to their T^{3} scaling with the simulation duration T. Recently, T^{2} scaling was achieved with the generalized Kadanoff-Baym ansatz (GKBA), for second-order Born (SOA) selfenergies, which has substantially extended the scope of NEGF simulations. Here we demonstrate that GKBA-NEGF simulations can be performed with order T^{1} scaling, both for SOA and GW selfenergies, and point out the remarkable capabilities of this approach.The dynamics of strongly correlated fermions following an external excitation reveals extremely rich collective quantum effects. Examples are fermionic atoms in optical lattices, electrons in correlated materials, and dense quantum plasmas. Presently, the only quantum-dynamics approach that rigorously describes these processes in two and three dimensions is the nonequilibrium Green functions (NEGF) method. However, NEGF simulations are computationally expensive due to their T^{3} scaling with the simulation duration T. Recently, T^{2} scaling was achieved with the generalized Kadanoff-Baym ansatz (GKBA), for second-order Born (SOA) selfenergies, which has substantially extended the scope of NEGF simulations. Here we demonstrate that GKBA-NEGF simulations can be performed with order T^{1} scaling, both for SOA and GW selfenergies, and point out the remarkable capabilities of this approach.

arXiv:1909.11489Physical Review LettersFeb 19, 2020100 citations

Advances in Quantum Dynamics

Geoffrey L. Price, Baker, B. Mitchell, Palle E. T. Jørgensen +1 more

Contemporary mathematics - American Mathematical SocietyJan 1, 200331 citations

Nonequilibrium Quantum Dynamics of Many-Body Systems

Léa Ferreira dos Santos, Eduardo Jonathan Torres-Herrera

arXiv:1706.02031Understanding complex systemsNov 18, 201712 citations

N_\mathrm{t}

. This scaling bottleneck could recently be overcome by introducing the G1--G2 scheme that is linear in

N_\mathrm{t}

, but requires propagation of a two-particle correlation function and may suffer from numerical instabilities. This has restricted simulations to small systems with

N_\mathrm{b} \sim 10^2

basis states. Here we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted

δ

NEGF, that represents dynamical two-particle correlations through fluctuations of field-operator products,

δ\hat G

. This 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 trajectories. 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

N_\mathrm{b}\sim 10^4

. We benchmark

δ

NEGF 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 ultrafast relaxation in graphene nanoribbon heterostructures with long-range Coulomb interactions. These results establish

δ

NEGF as a scalable route to dynamical self-energy simulations of large, spatially inhomogeneous correlated quantum systems beyond the reach of existing NEGF implementations.