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Register a new userPhysical and unphysical regimes of self-consistent many-body perturbation theory
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In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order $N$ and plugged into the Dyson equation, which is then solved for the propagator $G_N$. For two simple examples of fermionic models -- the Hubbard atom at half filling and its zero space-time dimensional simplified version -- we find that $G_N$ converges when $Ntoinfty$ to a limit $G_infty,$, which coincides with the exact physical propagator $G_{rm exact} ,$ at small enough coupling, while $G_infty eq G_{rm exact} ,$ at strong coupling. We also demonstrate that it is possible to discriminate between these two regimes thanks to a criterion which does not require the knowledge of $G_{rm exact} ,$, as proposed in [Rossi et al., PRB 93, 161102(R) (2016)].
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Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2-d, a highly unconventional quadruple-fermion non-Cooper-pair order parameter is discovered.
Many-body theory is largely based on self-consistent equations that are constructed in terms of the physical quantity of interest itself, for example the density. Therefore, the calculation of important properties such as total energies or photoemission spectra requires the solution of non-linear equations that have unphysical and physical solutions. In this work we show in which circumstances one runs into an unphysical solution, and we indicate how one can overcome this problem. Moreover, we solve the puzzle of when and why the interacting Greens function does not unambiguously determine the underlying system, given in terms of its potential, or non-interacting Greens function. Our results are general since they originate from the fundamental structure of the equations. The absorption spectrum of lithium fluoride is shown as one illustration, and observations in the literature for some widely used models are explained by our approach. Our findings apply to both the weak and strong-correlation regimes. For the strong-correlation regime we show that one cannot use the expressions that are obtained from standard perturbation theory, and we suggest a different approach that is exact in the limit of strong interaction.
Many-body perturbation theory is often formulated in terms of an expansion in the dressed instead of the bare Greens function, and in the screened instead of the bare Coulomb interaction. However, screening can be calculated on different levels of approximation, and it is important to define what is the most appropriate choice. We explore this question by studying a zero-dimensional model (so called one-point model) that retains the structure of the full equations. We study both linear and non-linear response approximations to the screening. We find that an expansion in terms of the screening in the random phase approximation is the most promising way for an application in real systems. Moreover, by making use of the nonperturbative features of the Kadanoff-Baym equation for the one-body Greens function, we obtain an approximate solution in our model that is very promising, although its applicability to real systems has still to be explored.
The carrier-density dependence of the photoemission spectrum of the Holstein many-polaron model is studied using cluster perturbation theory combined with an improved cluster diagonalization by Chebychev expansion.
The bandstructure of gold is calculated using many-body perturbation theory (MBPT). Different approximations within the GW approach are considered. Standard single shot G0W0 corrections shift the unoccupied bands up by ~0.2 eV and the first sp-like occupied band down by ~0.4 eV, while leaving unchanged the 5d occupied bands. Beyond G0W0, quasiparticle self-consistency on the wavefunctions lowers the occupied 5d bands by 0.35 eV. Globally, many-body effects achieve an opening of the interband gap (5d-6sp gap) of 0.35 to 0.75 eV approaching the experimental results. Finally, the quasiparticle bandstructure is compared to the one obtained by the widely used HSE (Heyd, Scuseria, and Ernzerhof) hybrid functional.
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