Motion of an impurity in a two-leg ladder

TL;DR

This paper analytically investigates the dynamics of an impurity in a two-leg ladder system interacting with fermionic baths, revealing an orthogonality catastrophe and effects of differing interaction strengths on transport.

Contribution

It provides exact analytical results for the impurity's Green's function in a two-leg ladder, highlighting the impact of interaction asymmetry and the orthogonality catastrophe.

Findings

Long-time behavior dominated by orthogonality catastrophe.

Differences in interaction strengths lead to subleading corrections.

No significant difference between intra- and inter-leg Green's functions long-term.

Abstract

We study the motion of an impurity in a two-leg ladder interacting with two fermionic baths along each leg, a simple model bridging cold atom quantum simulators with an idealised description of the basic transport processes in a layered heterostructure. Using the linked-cluster expansion we obtain exact analytical results for the single-particle Green's function and find that the long-time behaviour is dominated by an intrinsic orthogonality catastrophe associated to the motion of the impurity in each one-dimensional chain. We explore both the case of two identical legs as well as the case where the legs are characterised by different interaction strengths: in the latter case we observe a subleading correction which can be relevant for intermediate-time transport at an interface between different materials. In all the cases we do not find significant differences between the intra- and inter-leg Green's functions in the long-time limit.