Strong-coupling solver for the quantum impurity model

We propose a fast impurity solver for the general quantum impurity model based on the perturbation theory around the atomic limit, which can be used in combination with the local density approximation (LDA) and the dynamical mean-field theory (DMFT). We benchmark the solver in the two-band Hubbard model within DMFT against quantum Monte Carlo (QMC) and numerical renormalization-group (NRG) results. We find that the solver works very well in the paramagnetic Mott insulator phase. We also apply this impurity solver to the DMFT study of the antiferromagnetic phase transition in the unfrustrated Bethe lattice. The Neel temperature obtained by the fast impurity solver agrees very well with the QMC results in the large Hubbard U limit. The method is a promising tool to be used in combination with the $\mathrm{LDA}+\mathrm{DMFT}$ to study Mott insulators starting from first principles.

Figure 1

The comparison of QMC and DMFT with atomic solver for the two-band Hubbard model with $U=6$, $\mu =0$, $T=0.125$, and half bandwidth $D=1$.

Figure 2

The comparison of QMC and DMFT with the atomic solver for the two-band Hubbard model with $U=4$, $\mu =0$, $T=0.125$ and half bandwidth $D=1$.

Figure 3

(Color online) The comparison of the Neel temperature obtained by QMC, IPT, Hatree-Fock, and the atomic solver for a half-filled single-band Hubbard model with half bandwidth $D=1$.

Figure 4

(Color online) The spectral function of the one-band Hubbard model on the Bethe lattice for various values of $U$ compared with the NRG results (taken from Ref. 20).

Figure 5

(Color online) The DMFT spectral function obtained by using self-energy from Eq. (24) compared with the NRG results.