Dynamical Screening in Correlated Electron Materials

We present an efficient method for incorporating a dynamically screened interaction into the single-site dynamical mean field approximation widely used to treat correlation physics. Model system calculations are presented which capture the essential features of the frequency-dependent interactions previously obtained for Gd, Ni, ${\mathrm{SrVO}}_3$ and other compounds. Dynamical screening is shown to shift the metal-insulator phase boundary, to change the spectral function near the Mott-Hubbard gap edge, and to renormalize the quasiparticle weight. A multipeak spectral function is found, with shakeoff (Hubbard) bands which are generically neither separated by the screened nor by the unscreened interaction energy, implying that the common practice of extracting the Hubbard $U$ from the energies of features in photoemission and inverse photoemission spectra requires reexamination.

Figure 1

Illustration of an order $n=4$ diagram for the one orbital Hubbard model. Empty (full) circles and squares represent $V^{†}$ ($V$) hybridization events. Dashed lines indicate interactions $K(\tau )$ connecting all pairs of hybridization events.

Figure 2

Left panels: phase diagram in the space of bare interaction $U$ and screening strength $\lambda$ ($\alpha$) for indicated values of the screening frequency ${\omega }^{\prime }$ (${\omega }_c$). Upper panel: model (i); lower panel, model (ii). Heavy lines with open symbols: transition from metal to Mott insulator. Light lines with open symbols: transition from metal to bipolaronic insulator. Light lines with full symbols: transition from Mott insulator to bipolaronic insulator. Dashed lines: screening strength at which the screened interaction $U_{\mathrm{scr}}$ changes sign. Right panels: phase diagram in the space of screened and bare interaction.

Figure 3

Evolution of the spectral function across the metal-insulator transition for model (i). Top panel: effect of the variation of the screening strength at fixed $U=10$, ${\omega }^{\prime }=3$. Bottom panel: effect of the variation of the screening frequency at fixed $U=8$ and $U_{\mathrm{scr}}=3$. Light (heavy) dashed line: spectrum of the unscreened model for $U=8$ ($U=3$). Inset: frequency-dependent interaction $\mathrm{Re}U(\omega )=U+\mathrm{Re}W(\omega )$.

Figure 4

Model (ii): evolution of the spectral function for $U=8$, $U_{\mathrm{scr}}=3$ and indicated values of ${\omega }_c$. Light (heavy) dashed line: spectrum of the unscreened model for $U=8$ ($U=3$). Inset: $\mathrm{Re}U(\omega )=U+\mathrm{Re}W(\omega )$.