Adiabatic Preparation of a Correlated Symmetry‐Broken Initial State with the Generalized Kadanoff–Baym Ansatz

Abstract

A fast time propagation method for nonequilibrium Green's functions (NEGF) based on the generalized Kadanoff-Baym Ansatz (GKBA) is applied to a lattice system with a symmetry-broken equilibrium phase, namely an excitonic insulator (EI). The adiabatic preparation of a correlated symmetrybroken initial state from a Hartree-Fock wave function within GKBA is assessed by comparing with a solution of the imaginary-time Dyson equation. It is found that it is possible to reach a symmetry-broken correlated initial state with nonzero excitonic order parameter by the adiabatic switching (AS) procedure. It is discussed under which circumstances this is possible in practice within reasonably short switching times.

Achieving the Scaling Limit for Nonequilibrium Green Functions Simulations

“…Eqs. (6) and (7) below] have become a powerful tool for studying the quantum dynamics in many fields, including optically excited semiconductors [23][24][25], excitonic insulators [26], quantum transport and molecular junctions [27,28], laserexcited plasmas [29,30] and atoms [10,13], strongly correlated electrons [22] and fermionic atoms in optical lattices [15,31]. In recent years, significant effort was devoted to improve the GKBA, see, e.g., Refs.…”

A Scalable Numerical Approach to the Solution of the Dyson Equation for the Non‐Equilibrium Single‐Particle Green's Function

“…The details implementation of the numerical solution of the GKBA can be found in ref. . Specifically, we look at the imbalance of particles between even and odd sites as a figure of merit of the global behavior of the system and of its ergodic properties at the single‐particle level.…”

“…The GKBA approach is particularly appealing and the structure of the equation is completely general in the sense that it can be applied to different quantum systems, both closed and open as already pointed out in the original paper. For this reason there is a lot of activity in developing it and trying to extend its range of applicability to different physical scenarios . Unfortunately, the GKBA suffers from three major drawbacks: 1) the single particle spectrum is often calculated only at the Hartree‐Fock regime; 2) the choice of the self‐energy is limited to the second‐Born one (or truncated higher order approaximation such as in the T‐matrix case) in order not to lose the nice single‐time structure, and consequently its appealing scaling in computation time with both the system size and the number time steps; 3) the initial state of the system has to be chosen uncorrelated (non‐interacting) or requires an extra initial evolution for the adiabatic preparation of an initially correlated state.…”

Efficient computation of the second-Born self-energy using tensor-contraction operations

“…The lesser Green's function or the 1RDM can then be solved from Eq. (2.8) by a numerical time-stepping algorithm and using the symmetry property G > (t,t) = −i+G < (t,t) [25,36,48].…”

“…However, using the GKBA, the initial correlations collision integral, I ic , is usually neglected due to the lack of a GKBA-like expression for the mixed components G , and Σ , c . The correlated initial state therefore needs to be prepared by starting with an uncorrelated (or HF) system and slowly switching on the interaction (adiabatic switching procedure) [25,36,48,51]. However, the inclusion of the initial correlations has been shown to be possible also within GKBA [52][53][54].…”