Assisted hopping in the Anderson impurity model: A flow equation study

TL;DR

This paper employs flow equations to analyze how assisted hopping influences the Anderson impurity model, revealing renormalized parameters and a potential shift towards local pairing tendencies.

Contribution

It introduces a flow equation approach to study assisted hopping effects, showing how the model parameters evolve and indicating a possible transition to an attractive regime.

Findings

Renormalized on-site energy and interaction parameters are obtained.

Flow towards an attractive Anderson model for certain parameters.

Indication of local pairing fluctuations emerging from assisted hopping.

Abstract

We investigate the effect of assisted hopping in the Anderson impurity model. We use the flow equation method, which, by means of unitary transformations, generates a sequence of Hamiltonians in order to eliminate the assisted hopping terms. This approach yields a renormalized on-site energy $\epsilon_d^*$, a renormalized correlation energy $U^*$ and other terms, which include pair hopping. For some parameter values, the initial Hamiltonian flows towards an attractive Anderson model. We argue that this result implies a tendency towards local pairing fluctuations.