Functional renormalization group treatment of the 0.7 analog in quantum point contacts

Abstract

We combine two recently established methods, the extended Coupled-Ladder Approximation (eCLA) [Phys. Rev. B 95, 035122 (2017)] and a dynamic Keldysh functional Renormalization Group (fRG) approach for inhomogeneous systems [Phys. Rev. Lett. 119, 196401 (2017)] to tackle the problem of finite-ranged interactions in quantum point contacts (QPCs) at finite temperature. Working in the Keldysh formalism, we develop an eCLA framework, proceeding from a static to a fully dynamic description. Finally, we apply our new Keldysh eCLA method to a QPC model with finite-ranged interactions and show evidence that an interaction range comparable to the length of the QPC might be an essential ingredient for the development of a pronounced 0.7-shoulder in the linear conductance. We also discuss problems arising from a violation of a Ward identity in second-order fRG.

Second-order functional renormalization group approach to quantum wires out of equilibrium

“…In this work, we aim to account for all second-order terms. This has so far only been achieved in thermal equilibrium [21][22][23][24][25] as well as for the singleimpurity Anderson model out of equilibrium [26].…”

“…(26) can be carried out analytically. The integral that appears in the selfenergy flow equation (25), however, needs to be performed numerically. It is thus necessary to discretize the frequency argument of (ω).…”

“…(2) Split up the indices 1 , 1 into disjoint sets (see below). On each node, compute the right-hand side of the self-energy flow equation (25) for a given set and for all frequencies ω. To this end, perform the following steps:…”

“…The only quantity that needs to be sent across nodes is the self-energy, which feeds back into its own flow equation (25). Note that the corresponding amount of data is small, and MPI parallelization is highly efficient.…”

“…In contrast to previous approaches to this problem [17], we incorporate second-order contributions and can therefore describe inelastic processes and heating effects. Due to the significant numerical cost, second-order FRG schemes have so far only been implemented for electronic systems in thermal equilibrium [21][22][23][24][25] as well as for the single-impurity Anderson model out of equilibrium [26].…”