Efficient evaluation of the polarization function in dynamical mean-field theory

@article{Krien2019EfficientEO,
  title={Efficient evaluation of the polarization function in dynamical mean-field theory},
  author={Friedrich Krien},
  journal={Physical Review B},
  year={2019}
}
  • F. Krien
  • Published 9 January 2019
  • Physics
  • Physical Review B
The dynamical susceptibility of strongly correlated electronic systems can be calculated within the framework of the dynamical mean-field theory (DMFT). The required measurement of the four-point vertex of the auxiliary impurity model is however costly and restricted to a finite grid of Matsubara frequencies, leading to a cutoff error. It is shown that the propagation of this error to the lattice response function can be minimized by virtue of an exact decomposition of the DMFT polarization… 

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References

SHOWING 1-10 OF 76 REFERENCES

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition.

Local electronic correlation at the two-particle level

Electronic-correlated systems are often well described by dynamical mean field theory (DMFT). While DMFT studies have mainly focused hitherto on one-particle properties, valuable information is also

Improved Estimators for the Self-Energy and Vertex Function in Hybridization Expansion Continuous-Time Quantum Monte Carlo Simulations

measurement procedure for the self-energy and vertex function of the Anderson impurity model within the hybridization expansion continuous-time quantum Monte Carlo algorithm. The method is based on

Conservation in two-particle self-consistent extensions of dynamical mean-field theory

Extensions of dynamical mean-field theory (DMFT) make use of quantum impurity models as nonperturbative and exactly solvable reference systems which are essential to treat the strong electronic

Collective charge excitations of strongly correlated electrons, vertex corrections, and gauge invariance

We consider the collective, long-wavelength charge excitations in correlated media in presence of short- and long-range forces. As an example for the case of a short-range interaction, we examine the

Non-Perturbative Many-Body Approach to the Hubbard Model and Single-Particle Pseudogap

A new approach to the single-band Hubbard model is described in the general context of many-body theories. It is based on enforcing conservation laws, the Pauli principle and a number of crucial

Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study

In this paper, we investigate how nonlocal correlations affect, selectively, the physics of correlated electrons over different energy scales, from the Fermi level to the band edges. This goal is

Efficient Bethe-Salpeter equation treatment in dynamical mean-field theory

We present here two alternative schemes designed to correct the high-frequency truncation errors in the numerical treatment of the Bethe-Salpeter equations. The schemes are applicable to all

Magnetic properties of the t - J model in the dynamical mean-field theory

We present a theory for the spin correlation function of the t - J model in the framework of the dynamical mean-field theory. Using this mapping between the lattice and a local model we are able to
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