Motion of an impurity in a two-leg ladder

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 idealized 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 behavior 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 characterized 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 interleg Green's functions in the long-time limit.

Automated summary

The study focuses on the motion of an impurity in a two-leg ladder interacting with fermionic baths along each leg, bridging cold atom quantum simulators with an idealized description of transport processes in a layered heterostructure. Exact analytical results for the single-particle Green's function are obtained using the linked-cluster expansion, revealing that the long-time behavior is dominated by an intrinsic orthogonality catastrophe. Differences between intra- and interleg Green's functions are not significant in the long-time limit, but a subleading correction observed in the case of legs with different interaction strengths may be relevant for intermediate-time transport at material interfaces.