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

TL;DR

This study models nonequilibrium effects in an infinite-dimensional Hubbard lattice, analyzing how quasi-particle spectra evolve with bias and temperature using perturbation theory, revealing critical points where quasi-particles vanish near the Mott transition.

Contribution

It introduces a nonequilibrium dynamical mean-field theory framework with a superposition of electronic states and applies second-order perturbation theory to explore quasi-particle behavior.

Findings

Quasi-particle states disappear at bias comparable to their energy scale.

Critical Coulomb interaction U_d exists below U_c where quasi-particles are abruptly destroyed.

Quasi-particle destruction follows a specific relation involving bias, temperature, and energy scale.

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 $\varepsilon^0_{QP}$ disappear at $\Phi\sim\varepsilon^0_{QP}$ 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 $(\varepsilon^0_{QP})^2\sim a(\pi k_BT_c)^2+ b\Phi_c^2$ with the critical temperature $T_c$, the critical bias $\Phi_c$ and the numerical constants $a$ and $b$ at the order of unity.