Real-time Dyson expansion for the nonequilibrium $GW$ approximation: Correlated spectra and dependence on the reference propagatorReal-time Dyson expansion for the nonequilibrium $GW$ approximation: Correlated spectra and dependence on the reference propagator

Erik Schroedter, Jan‐Philip Joost, M. Bönitz +1 more

Electronic spectra provide direct insight into the excitations and correlations of condensed matter systems. Their description requires electron correlations beyond mean field. In equilibrium, the $GW$ approximation has become the method of choice for many materials. Extending this approximation to nonequilibrium, however, is challenging. Full two-time $GW$ simulations within the nonequilibrium Green's functions approach scale at least cubically with propagation time, whereas improved scaling schemes such as time-local (adiabatic) approximations or the generalized Kadanoff--Baym ansatz usually retain only mean-field character in the spectra. The recently introduced real-time Dyson expansion recovers dynamical correlations in the spectrum at time-linear cost, but has so far been restricted to the second-order Born approximation with mean-field reference propagators. Here we formulate and implement the RT-DE for the nonequilibrium $GW$ self-energy with reference propagators of general form whose off-diagonal evolution is time local. In particular, we assess Hartree--Fock propagators, propagators with statically screened exchange with nonequilibrium screening, and a correlated propagator based on the Hartree--Fock GKBA. Benchmarks against exact diagonalization for a driven two-band lattice model with long-range interactions show that the mean-field and statically screened references yield the most accurate spectra, including satellite structures absent at mean-field level, whereas the GKBA-based approach best captures scattering-induced occupation dynamics, but artificially broadens and splits spectral peaks. When applied to large systems that are beyond the reach of exact methods, the scheme resolves the excitonic replica of the valence band and satellites identified as exciton shake-up, as well as their reshaping with increasing excitation density.Electronic spectra provide direct insight into the excitations and correlations of condensed matter systems. Their description requires electron correlations beyond mean field. In equilibrium, the $GW$ approximation has become the method of choice for many materials. Extending this approximation to nonequilibrium, however, is challenging. Full two-time $GW$ simulations within the nonequilibrium Green's functions approach scale at least cubically with propagation time, whereas improved scaling schemes such as time-local (adiabatic) approximations or the generalized Kadanoff--Baym ansatz usually retain only mean-field character in the spectra. The recently introduced real-time Dyson expansion recovers dynamical correlations in the spectrum at time-linear cost, but has so far been restricted to the second-order Born approximation with mean-field reference propagators. Here we formulate and implement the RT-DE for the nonequilibrium $GW$ self-energy with reference propagators of general form whose off-diagonal evolution is time local. In particular, we assess Hartree--Fock propagators, propagators with statically screened exchange with nonequilibrium screening, and a correlated propagator based on the Hartree--Fock GKBA. Benchmarks against exact diagonalization for a driven two-band lattice model with long-range interactions show that the mean-field and statically screened references yield the most accurate spectra, including satellite structures absent at mean-field level, whereas the GKBA-based approach best captures scattering-induced occupation dynamics, but artificially broadens and splits spectral peaks. When applied to large systems that are beyond the reach of exact methods, the scheme resolves the excitonic replica of the valence band and satellites identified as exciton shake-up, as well as their reshaping with increasing excitation density.

arXiv:2609.08932Sep 8, 20260 citations

Dynamical mean-field-driven spinor-condensate physics beyond the single-mode approximation

Jianwen Jie, Shan Zhong, Qimin Zhang +7 more

$^{23}\mathrm{Na}$ spin-1 Bose-Einstein condensates are used to experimentally demonstrate that mean-field physics beyond the single-mode approximation can be relevant during the nonequilibrium dynamics. The experimentally observed spin oscillation dynamics and associated dynamical spatial structure formation confirm theoretical predictions that are derived by solving a set of coupled mean-field Gross-Pitaevskii equations [J. Jie et al., Phys. Rev. A 102, 023324 (2020)]. The experiments rely on microwave dressing of the $f=1$ hyperfine states, where $f$ denotes the total angular momentum of the $^{23}\mathrm{Na}$ atom. The fact that physics beyond the single-mode approximation at the mean-field level, i.e., spatial mean-field dynamics that distinguishes the spatial density profiles associated with different Zeeman levels, can, in certain parameter regimes, have a pronounced effect on the dynamics when the spin healing length is comparable to or larger than the size of the Bose-Einstein condensate has implications for using Bose-Einstein condensates as models for quantum phase transitions and spin squeezing studies as well as for nonlinear SU(1,1) interferometers.$^{23}\mathrm{Na}$ spin-1 Bose-Einstein condensates are used to experimentally demonstrate that mean-field physics beyond the single-mode approximation can be relevant during the nonequilibrium dynamics. The experimentally observed spin oscillation dynamics and associated dynamical spatial structure formation confirm theoretical predictions that are derived by solving a set of coupled mean-field Gross-Pitaevskii equations [J. Jie et al., Phys. Rev. A 102, 023324 (2020)]. The experiments rely on microwave dressing of the $f=1$ hyperfine states, where $f$ denotes the total angular momentum of the $^{23}\mathrm{Na}$ atom. The fact that physics beyond the single-mode approximation at the mean-field level, i.e., spatial mean-field dynamics that distinguishes the spatial density profiles associated with different Zeeman levels, can, in certain parameter regimes, have a pronounced effect on the dynamics when the spin healing length is comparable to or larger than the size of the Bose-Einstein condensate has implications for using Bose-Einstein condensates as models for quantum phase transitions and spin squeezing studies as well as for nonlinear SU(1,1) interferometers.

arXiv:2301.06461Physical Review AMay 11, 20236 citations

Non-equilibrium Dynamical Mean-Field Theory

Martin Eckstein

Springer eBooksJan 1, 20184 citations

Field-Theory Approaches to Nonequilibrium Dynamics

U. C. Täuber

arXiv:cond-mat/0511743Springer eBooksApr 11, 200761 citations

Nonequilibrium dynamics in the O(N) model to next-to-next-to-leading order in the 1/N expansion

Gert Aarts A, Anders Tranberg B

Nonequilibrium dynamics in quantum field theory has been studied extensively using truncations of the 2PI effective action. Both $1/N$ and loop expansions beyond leading order show remarkable improvement when compared to mean-field approximations. However, in truncations used so far, only the leading-order parts of the self-energy responsible for memory loss, damping and equilibration are included, which makes it difficult to discuss convergence systematically. For that reason we derive the real and causal evolution equations for an $O(N)$ model to next-to-next-to-leading order in the 2PI- $1/N$ expansion. Because of the appearance of internal vertices the resulting equations appear intractable for a full-fledged $3+1$ dimensional field theory. Instead, we solve the closely related three-loop approximation in the auxiliary-field formalism numerically in $0+1$ dimensions (quantum mechanics) and compare to previous approximations and the exact numerical solution of the Schr\"odinger equation.Nonequilibrium dynamics in quantum field theory has been studied extensively using truncations of the 2PI effective action. Both $1/N$ and loop expansions beyond leading order show remarkable improvement when compared to mean-field approximations. However, in truncations used so far, only the leading-order parts of the self-energy responsible for memory loss, damping and equilibration are included, which makes it difficult to discuss convergence systematically. For that reason we derive the real and causal evolution equations for an $O(N)$ model to next-to-next-to-leading order in the 2PI-$1/N$ expansion. Because of the appearance of internal vertices the resulting equations appear intractable for a full-fledged $3+1$ dimensional field theory. Instead, we solve the closely related three-loop approximation in the auxiliary-field formalism numerically in $0+1$ dimensions (quantum mechanics) and compare to previous approximations and the exact numerical solution of the Schr\"odinger equation.

arXiv:hep-th/0604156Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJul 6, 200629 citations

Real-time Dyson expansion for the nonequilibrium

GW

approximation: Correlated spectra and dependence on the reference propagator

Electronic spectra provide direct insight into the excitations and correlations of condensed matter systems. Their description requires electron correlations beyond mean field. In equilibrium, the

GW

approximation has become the method of choice for many materials. Extending this approximation to nonequilibrium, however, is challenging. Full two-time

GW

simulations within the nonequilibrium Green's functions approach scale at least cubically with propagation time, whereas improved scaling schemes such as time-local (adiabatic) approximations or the generalized Kadanoff--Baym ansatz usually retain only mean-field character in the spectra. The recently introduced real-time Dyson expansion recovers dynamical correlations in the spectrum at time-linear cost, but has so far been restricted to the second-order Born approximation with mean-field reference propagators. Here we formulate and implement the RT-DE for the nonequilibrium

GW

self-energy with reference propagators of general form whose off-diagonal evolution is time local. In particular, we assess Hartree--Fock propagators, propagators with statically screened exchange with nonequilibrium screening, and a correlated propagator based on the Hartree--Fock GKBA. Benchmarks against exact diagonalization for a driven two-band lattice model with long-range interactions show that the mean-field and statically screened references yield the most accurate spectra, including satellite structures absent at mean-field level, whereas the GKBA-based approach best captures scattering-induced occupation dynamics, but artificially broadens and splits spectral peaks. When applied to large systems that are beyond the reach of exact methods, the scheme resolves the excitonic replica of the valence band and satellites identified as exciton shake-up, as well as their reshaping with increasing excitation density.

^{23}\mathrm{Na}

spin-1 Bose-Einstein condensates are used to experimentally demonstrate that mean-field physics beyond the single-mode approximation can be relevant during the nonequilibrium dynamics. The experimentally observed spin oscillation dynamics and associated dynamical spatial structure formation confirm theoretical predictions that are derived by solving a set of coupled mean-field Gross-Pitaevskii equations [J. Jie et al., Phys. Rev. A 102, 023324 (2020)]. The experiments rely on microwave dressing of the

f=1

hyperfine states, where

f

denotes the total angular momentum of the

^{23}\mathrm{Na}

atom. The fact that physics beyond the single-mode approximation at the mean-field level, i.e., spatial mean-field dynamics that distinguishes the spatial density profiles associated with different Zeeman levels, can, in certain parameter regimes, have a pronounced effect on the dynamics when the spin healing length is comparable to or larger than the size of the Bose-Einstein condensate has implications for using Bose-Einstein condensates as models for quantum phase transitions and spin squeezing studies as well as for nonlinear SU(1,1) interferometers.

Nonequilibrium dynamics in quantum field theory has been studied extensively using truncations of the 2PI effective action. Both

1/N

and loop expansions beyond leading order show remarkable improvement when compared to mean-field approximations. However, in truncations used so far, only the leading-order parts of the self-energy responsible for memory loss, damping and equilibration are included, which makes it difficult to discuss convergence systematically. For that reason we derive the real and causal evolution equations for an

O(N)

model to next-to-next-to-leading order in the 2PI-

1/N

expansion. Because of the appearance of internal vertices the resulting equations appear intractable for a full-fledged

3+1

dimensional field theory. Instead, we solve the closely related three-loop approximation in the auxiliary-field formalism numerically in

0+1

dimensions (quantum mechanics) and compare to previous approximations and the exact numerical solution of the Schr\"odinger equation.