Validity of the local approximation in iron pnictides and chalcogenides

We introduce a methodology to treat different degrees of freedom at different levels of approximation. We use cluster DMFT (dynamical mean field theory) for the $t_{2g}$ electrons and single site DMFT for the $e_g$ electrons to study the normal state of the iron pnictides and chalcogenides. In the regime of moderate mass renormalizations, the self-energy is very local, justifying the success of single site DMFT for these materials and for other Hunds metals. We solve the corresponding impurity model with CTQMC (continuous time quantum Monte Carlo) and find that the minus sign problem is not severe in regimes of moderate mass renormalization.

Figure 1

Left panel: Orbital character of the Fermi surface in the unfolded Brillouin zone of the tight-binding Hamiltonian [47] used in this work. Right panel: Tiling of the Brillouin zone in two patches ${\mathcal{P}}_{+}$ and ${\mathcal{P}}_{-}$, enclosing the holes pockets at $\mathrm{\Gamma }$ and $M$ and the electron pockets at $X$ and $Y$, respectively. This patching is compatible with the lattice symmetries.

Figure 2

Comparison of the $t_{2g}$ self-energy obtained by DMFT (real/imaginary part with thin/bold lines) and DCA (local/nonlocal part in red/blue and real/imaginary part with crosses/circles). All self-energies are diagonal in orbital space (see Appendix). The left panels show the degenerate $yz,zx$ entries and the right panel shows the $xy$ entry. The temperature is $T=174\text{K}$. In the upper panels $(U,\tilde{U})=(4.5,4.5)$ and $(J,\tilde{J})=(0.45,0.375)$ while in the lower panels $(U,\tilde{U})=(10.125,9)$ and $(J,\tilde{J})=(0,0)$.

Figure 3

Impurity spin susceptibility [see Eq. (3)] for DMFT (red squares) and DCA (blue circles) for parameters $(U,\tilde{U})=(4.5,4.5)$ and $(J,\tilde{J})=(0.45,0.375)$. The upper panel plots the susceptibility as a function of Matsubara frequencies for $T=174\text{K}$. The lower panel plots the susceptibility as a function of the temperature for $i{\nu }_n=0$. The black diamonds display the ratio between the DMFT and DCA spin susceptibility, and its scale is displayed in the right $y$ axis.

Figure 4

Average sign in the CT-HYB simulations for the DCA impurity model, in the left panel for $(J,\tilde{J})=(0.45,0.375)$ as a function of the temperature and in the right panel for $T=174\text{K}$ as a function of the Hund's rule coupling [the values are $(J,\tilde{J})=(0.45,0.375)$, $(0.488,0.441)$, $(0.506,0.469)$, and $(0.525,0.51)$ from left to right]. The Coulomb repulsion is $(U,\tilde{U})=(4.5,4.5)$ in both panels. The CT-HYB simulations are carried out in the $\mathbf{K}$-space single particle basis, see the Appendix.

Figure 5

Self-energies (real/imaginary part with open/filled symbols) of the $t_{2g}$ orbitals obtained with DMFT for the model with interactions applied to all $d$-shell orbitals (red circles) and for the effective $t_{2g}$ model (blue diamonds). In the latter case, the Hartree-Fock constant ${\mathrm{\Sigma }}^{\text{HF}}$ is added. The parameters are $T=174\text{K}$, $(U,\tilde{U})=(4.5,4.5)$, and $(J,\tilde{J})=(0.45,0.375)$.