Nonequilibrium Green Functions in Linear Time

The selfconsistent theoretical treatment of correlation and quantum effects in nonequilibrium beyond one-dimensional systems is a particular challenge that has been successfully attacked with nonequilibrium Green functions (NEGF) methods [1]. However, NEGF simulations are hampered by a cubic scaling of the computation time with the number of time steps N_t. Recently, a dramatic acceleration has been achieved within the G1–G2 scheme [2] by transforming the NEGF equations, within the Hartree-Fock Generalized Kadanoff–Baym ansatz (GKBA) [3], to a time-local form for the single-particle and two-particle Green functions. A detailed discussion of the method and its application to a variety of selfenergies including particle-particle and particle-hole T matrix, GW, and the dynamically screened ladder (DSL) was presented recently [4]. Due to its relation to the single-time BBGKY hierarchy, the G1–G2 scheme can benefit from a variety of well-established techniques of two-particle reduced density matrix (2RDM) theory, such as enforcing contraction consistency or a purification of the dynamics, to further improve its accuracy and numerical stability [5]. A drawback of the G1–G2 scheme is the memory cost needed to store the two-particle Green function. This can be significantly relieved by using a recently developed alternative stochastic approach to the G1–G2 scheme [6]. We present first results for the stochastic GW approximation.

[1] N. Schlünzen et al., Phys. Rev. B 93, 035107 (2016)

[2] N. Schlünzen et al., Phys. Rev. Lett. 124, 076601 (2020)

[3] P. Lipavský et al., Phys. Rev. B 34, 6933 (1986)

[4] J.-P. Joost et al., Phys. Rev. B 101, 245101 (2020)

[5] J.-P. Joost et al., Phys. Rev. B 105, 165155 (2022)

[6] E. Schroedter et al., Cond. Matt. Phys. 25, 23401 (2022)