Extended dynamic Mott transition in the two-band Hubbard model out of equilibrium

We reformulate the time-dependent Gutzwiller approximation by M. Schiró and M. Fabrizio, [Phys. Rev. Lett. 105, 076401 (2010)] in the framework of slave-boson mean-field theory, which is used to investigate the dynamical Mott transition of the generic two-band Hubbard model at half filling upon an interaction quench. Interorbital fluctuations lead to notable changes with respect to the single-band case. The singular dynamical transition is replaced by a broad regime of long-lived fluctuations between metallic and insulating states, accompanied by intriguing precursor behavior. A mapping to a spin model proves helpful to analyze the different regions in terms of the evolution of an Ising-like order parameter. Contrary to the static case, singlet occupations remain vital in the Mott-insulating regime with finite Hund's exchange.

Figure 1

QP weight $Z\left(t\right)$ and occupation probability #$p$ of local sectors with particles $p=0$,1,2 for the interaction quench to $U_f=0.2$. Dotted lines denote period of local states oscillations. The inset shows the Fourier transform (absolute value of Fourier coefficients in logarithmic units) of $Z\left(t\right)$. See the text for use of the circles.

Figure 2

Top: Main-frequency evolution with $U_f$ for $U^{\prime }=U^{\prime \prime }=0$ and $U^{\prime }=U^{\prime \prime }=U$ from Fourier transforming $Z\left(t\right)$. The dotted lines separate three different regions (see text and Fig. 4). Bottom: Time-averaged $Z$ as a function of $U_f$. Dashed lines mark the equilibrium behavior with the black dot denoting the associated Mott-critical point. Gray hashed area indicates precursor behavior.

Figure 3

Level diagram for the active frequencies in the case $U^{\prime }=U^{\prime \prime }=U$ within the different regimes dictated by $U_f$.

Figure 4

Order parameter $\overline{\langle S_x\rangle }$ for $U^{\prime }=U^{\prime \prime }=0$ (dashed) and $U^{\prime }=U^{\prime \prime }=U$ (full). Inset shows $\overline{\langle S_x\rangle }\left(T\right)$ in the three different regions. The quasidecoupled two-band case stabilizes only in regions I and III (divided by the vertical dashed line). Region II appears with interorbital terms. The precursor regime is visualized by the gray hashed area.

Figure 5

Time-averaged diagonal renormalization $R$ and QP weight $Z$ for $U/J=5$. Black dot marks the Mott-critical point of the associated equilibrium model. Insets show $\overline{R}\left(T\right)$ in the three different regions.

Figure 6

Time-averaged multiplet occupation probabilities for $U/J=5$ with the equilibrium probabilities (dashed lines) for comparison. The Mott-critical point of the associated equilibrium model is described by a black dot. Insets reveal explicit time evolution of multiplet occupation probabilities in different regions.