Symmetry breaking and restoration using the equation-of-motion technique for nonequilibrium quantum impurity models

Abstract

The description of the dynamics of correlated electrons in quantum impurity models is typically described within the nonequilibrium Green function formalism combined with a suitable approximation. One common approach is based on the equation-of-motion technique often used to describe different regimes of the dynamic response. Here, we show that this approach may violate certain symmetry relations that must be fulfilled by the definition of the Green functions. These broken symmetries can lead to unphysical behavior. To circumvent this pathological shortcoming of the equation-of-motion approach we provide a scheme to restore basic symmetry relations. Illustrations are given for the Anderson and double Anderson impurity models.

A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators

“…EOM formulated on the Keldysh contour has been used in the literature to describe transport in junctions by us 47,48 and others. 44,45,52,53 Two main weaknesses of the method are: 1. The necessity to make uncontrollable approximations in truncating the (in general infinite) chain of EOMs and 2.…”

“…We show that proper symmetrization, as discussed in Refs. 42,52,53, is built into the scheme. We also show explicitly that projection (orthogonalization) is crucial for proper description of a system coupled to the bath.…”

“…This is an example of the built-in symmetrization property of the formulation, which otherwise should be obtained within a stepby-step approach. 52,53 Note also that in the Coulomb blockade regime the EOM for the canonical Green function G (0) A1,A1 (τ, τ ′ ) can be solved directly (without a selfconsistent procedure). This is reminiscent of the similar observation in Ref.…”

Steady state conductance in a double quantum dot array: The nonequilibrium equation-of-motion Green function approach

“…To obtain a working closure one has to truncate the resulting set of equations and/or decouple the higher order GFs and express them via lower order ones. Recently it has been shown that such a procedure may lead to symmetries violations that the GFs must obey by definition 27 and a routine to restore back the symmetries was suggested.…”

“…24,25 However, questions regarding the validity of the EOM approach have been raised. 26,27 For example, it has been shown to violate the Friedel sum rule 28 near the Kondo regime 26 and basic Green function symmetry relations away from the Kondo regime. 27 In the latter case, symmetry relations can be restored and at least for the Anderson impurity model, 29 the approach recovers the Kondo peaks and provides a quantitative description of resonant transport.…”