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arXiv:0903.4838 · Physical Review B

Fast impurity solver based on equations of motion and decoupling

Qingguo Feng, Yu‐Zhong Zhang, Harald O. Jeschke

Published Jun 8, 2009• 19 citations
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Abstract

In this paper a fast impurity solver is proposed for dynamical mean-field theory (DMFT) based on a decoupling of the equations of motion for the impurity Green's function. The resulting integral equations are solved efficiently with a method based on genetic algorithms. The Hubbard and periodic Anderson models are studied with this impurity solver. The method describes the Mott metal-insulator transition and works for a large range of parameters at finite temperature on the real frequency axis. This makes it useful for the exploration of real materials in the framework of local-density $\text{approximation}+\text{DMFT}$.

DOI
10.1103/physrevb.79.235112

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This paper proposes an impurity solver for the dynamical mean field theory (DMFT) study of the Mott insulators, which is based on the second order perturbation of the hybridization function. After careful benchmarking with quantum Monte Carlo results on the anti-ferromagnetic phase of the Hubbard model, it concludes that this impurity solver can capture the main physical features in the strong coupling regime and can be a very useful tool for the LDA (local density approximation) + DMFT studies of the Mott insulators with long range order.
A fast impurity solver for the dynamical mean-field theory (DMFT) named two-mode approximation is proposed based on the Gutzwiller variational approach, which captures the main features of both the coherent and incoherent motion of the electrons. The solver works with real frequency at zero temperature and it provides directly the spectral function of the electrons. It can be easily generalized to multiorbital impurity problems with general on-site interactions, which makes it very useful in local-density approximation plus DMFT. Benchmarks on one- and two-band Hubbard models are presented, and the results agree well with those of exact diagonalization. Lastly a few cartoonlike five-band results are presented, showing that the present solver is really capable of dealing with multiband systems.
A nonperturbative quantum impurity solver is proposed based on a formally exact hierarchical equations of motion (HEOM) formalism for open quantum systems. It leads to quantitatively accurate evaluation of physical properties of strongly correlated electronic systems, in the framework of dynamical mean-field theory (DMFT). The HEOM method is also numerically convenient to achieve the same level of accuracy as that using the state-of-the-art numerical renormalization group impurity solver at finite temperatures. The practicality of the HEOM+DMFT method is demonstrated by its applications to the Hubbard models with Bethe and hypercubic lattice structures. We investigate the metal-insulator transition phenomena, and address the effects of temperature on the properties of strongly correlated lattice systems.
Dynamical Mean-Field Theory (DMFT) is among the most widely used techniques in computational condensed-matter physics, especially in addressing electron-electron interactions. In this regard, Quantum Monte Carlo may be considered as the most accurate DMFT impurity solver, but it usually requires a high numerical cost. On the contrary, lower numerical-cost technique, such as mean-field theory, often gives inaccurate results due to complete suppression of quantum fluctuations. In this study, we propose a new potentially low numerical-cost impurity solver taking a full account of fluctuation effects. Applying this new algorithm on Hubbard model, we formulate local self-energy that depends on the occupancy fluctuations. These fluctuations act as the semi-classical degree of freedom that needs to be integrated to obtain the averaged fully interacting Green functions. We test our algorithm by addressing temperature dependence of the density of states that reveals metal-insulator transition.