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

Abstract

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 ${\mu }_L$ and ${\mu }_R$. 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. $\Phi ={\mu }_L-{\mu }_R$. 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 ${\epsilon }_{QP}^0$ disappear at $\Phi \sim {\epsilon }_{QP}^0$ 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 $({\epsilon }_{QP}^0{)}^2\sim a(\pi k_B{T}_c{)}^2+b{\Phi }_c^2$ with the critical temperature $T_c$, the critical bias ${\Phi }_c$ and the numerical constants $a$ and $b$ at the order of unity.