Perturbation study of nonequilibrium quasi-particle spectra in an infinite-dimensional Hubbard lattice

A model for nonequilibrium dynamical mean-field theory is constructed for the infinite dimensional Hubbard lattice. We impose nonequilibrium by expressing the physical orbital as a superposition of a left-($L$) moving and right-($R$) moving electronic state with the respective chemical potential $μ_L$ and $μ_R$. Using the second-order iterative perturbation theory we calculate the quasi-particle properties as a function of the chemical potential bias between the $L$ and $R$ movers, i.e. $Φ= μ_L - μ_R$. The evolution of the nonequilibrium quasi-particle spectrum is mapped out as a function of the bias and temperature. The quasi-particle states with the renormalized Fermi energy scale $\varepsilon^0_{QP}$ disappear at $Φ\sim\varepsilon^0_{QP}$ in the low temperature limit. The second-order perturbation theory predicts that in the vicinity of the Mott-insulator transition at the Coulomb parameter $U=U_c$, there exists another critical Coulomb parameter $U_d$ ($<U_c$) such that, for $U_d<U<Uc$, quasi-particle states are destroyed abruptly when $(\varepsilon^0_{QP})^2\sim a(πk_BT_c)^2+ bΦ_c^2$ with the critical temperature $T_c$, the critical bias $Φ_c$ and the numerical constants $a$ and $b$ at the order of unity.