Mott Metal-Insulator Transition from Steady-State Density Functional Theory

We present a computationally efficient method to obtain the spectral function of bulk systems in the framework of steady-state density functional theory (i-DFT) using an idealized scanning tunneling microscope (STM) setup. We calculate the current through the STM tip and then extract the spectral function from the finite-bias differential conductance. The fictitious noninteracting system of i-DFT features an exchange-correlation (XC) contribution to the bias which guarantees the same current as in the true interacting system. Exact properties of the XC bias are established using Fermi-liquid theory and subsequently implemented to construct approximations for the Hubbard model. We show for two different lattice structures that the Mott metal-insulator transition is captured by i-DFT.

Figure 1

Model XC bias of Eq. (12) for the Bethe lattice for different values of $U$. Inset: Quasiparticle weights $Z$ from NRG of Ref. [52], our fit to the NRG data, as well as $\tilde{Z}$ according to Eq. (10). $W$ is the width of the band for $U=0$.

Figure 2

Spectral functions of the Hubbard model on the Bethe lattice for different interaction strengths obtained by i-DFT and compared with the NRG results of Ref. [53]. $W$ is the width of the band for $U=0$.

Figure 3

Spectral functions of the Hubbard model on the simple cubic lattice for different interaction strengths obtained by i-DFT and compared with the NRG results of Ref. [54].