Nonlocal Correlation Effects in dc and Optical Conductivity of the Hubbard Model

Abstract

Conductivity is one of the most direct probes of electronic systems, yet its theoretical description remains challenging in the presence of strong non-local correlations. In this Letter, we analyze the conductivity of the half-filled single-band Hubbard model and identify the role of spatial correlations across the Mott transition. We show that in the correlated metallic regime, an accurate description of the conductivity requires not only the correct spectral function but also the inclusion of complex multi-electron processes encoded in vertex corrections. The crossover to the Mott insulating regime is marked by a vanishing contribution of vertex corrections to the DC conductivity. However, in the Mott insulating case, vertex corrections remain significant for the optical conductivity.

Figures (4)

• Figure 1: Phase diagram of the half-filled single-band Hubbard model calculated using ${D\text{-}GW}$ in the $T$-$U$ plane. The blue curve represents the Néel transition and corresponds to the divergence of the spin susceptibility at the ${{\bf q} = (\pi, \pi)}$ point. The red curve indicates the gap opening at the AN point. The Mott transition (black curve) is characterized by a simultaneous gap opening at the N and AN points and is extrapolated to low temperatures by the dashed black line. The red dashed line is the extension of AN curve according to findings in Ref. PhysRevLett.132.236504. The orange stars indicate the two points at which the calculations are performed in Fig. \ref{['fig:fig2']} and Fig. \ref{['fig:fig3']} (a, b). The dashed gray lines depict the temperatures at which the the optical conductivity scans are performed in Fig. \ref{['fig:fig3']} (c).
• Figure 2: The momentum-resolved spectral function ${A({\bf k},\omega)}$ calculated close to the Néel transition (orange stars in Fig. \ref{['fig:phase']}) using ${D\text{-}GW}$ along the high-symmetry path of the Brillouin zone (${\Gamma=(0,0)}$, ${\text{X}=\text{AN}=(\pi,0)}$, ${\text{M}=(\pi,\pi)}$) in the metallic (${U=1.125}$, ${T = 0.036}$, panel (a)) and Mott insulating (${U=1.875}$, ${T = 0.027}$, panel (b)) phases. Panels (c) and (d) show the corresponding spectral functions at the $N$ (blue) and $AN$ (red) points in comparison with DMFT (black).
• Figure 3: The optical conductivity ${\sigma(\omega)}$ calculated close to the Néel transition (orange stars in Fig. \ref{['fig:phase']}) in the metallic (${U = 1.125}$, ${T = 0.036}$, panel (a)) and Mott insulating (${U = 1.875}$, ${T = 0.027}$, panel (b)) phases. The results are obtained using DMFT (dashed black), "bubble" ${D\text{-}GW}$ (blue), and "full" ${D\text{-}GW}$ (orange). The inset in (a) shows the low-frequency behavior of the conductivity. The arrows in panel (b) indicate the peaks and kinks originating from the optical transitions between the splittings in Hubbard bands due to strong magnetic fluctuations seen in Fig. \ref{['fig:fig2']} (d). Panel (c) shows the difference in the DC conductivity $\Delta{\sigma(\omega=0)}$ between the bubble and full results. The scans are performed for ${T=0.083}$ and ${T=0.036}$ depicted in Fig. \ref{['fig:phase']} by the dashed gray lines. The arrows in panel (c) indicate critical interactions ${U = 1.525}$ (${T=0.083}$) and ${U = 1.7}$ (${T=0.036}$) for the Mott transition shown in black dots in Fig. \ref{['fig:phase']}.
• Figure 4: The DC conductivity as a function of temperature calculated for ${n=0.85}$ at ${U=1.125}$ (a) and ${U=1.875}$ (b) using the DMFT (red) and "full" D-GW (orange) methods.