Nonequilibrium dynamical mean-field theory based on weak-coupling perturbation expansions: Application to dynamical symmetry breaking in the Hubbard model

摘要

We discuss the general formalism and validity of weak-coupling perturbationtheory as an impurity solver for nonequilibrium dynamical mean-field theory.The method is implemented and tested in the Hubbard model, using expansions upto fourth order for the paramagnetic phase at half filling and third order forthe antiferromagnetic and paramagnetic phase away from half filling. We explorevarious types of weak-coupling expansions and examine the accuracy andapplicability of the methods for equilibrium and nonequilibrium problems. Wefind that in most cases an expansion of local self-energy diagrams includingall the tadpole diagrams with respect to the Weiss Green's function(bare-diagram expansion) gives more accurate results than other schemes such asself-consistent perturbation theory using the fully interacting Green'sfunction (bold-diagram expansion). In the paramagnetic phase at half filling,the fourth-order bare expansion improves the result of the second-orderexpansion in the weak-coupling regime, while both expansions suddenly fail atsome intermediate interaction strength. The higher-order bare perturbation isespecially advantageous in the antiferromagnetic phase near half filling. Weuse the third-order bare perturbation expansion within the nonequilibriumdynamical mean-field theory to study dynamical symmetry breaking from theparamagnetic to the antiferromagnetic phase induced by an interaction ramp inthe Hubbard model. The results show that the order parameter, after an initialexponential growth, exhibits an amplitude oscillation around a nonthermal valuefollowed by a slow drift toward the thermal value. The transient dynamics seemsto be governed by a nonthermal critical point, associated with a nonthermaluniversality class, which is distinct from the conventional Ginzburg-Landautheory.