# Exactly solvable Majorana-Anderson impurity models

## TL;DR

This paper introduces exactly solvable Majorana-Anderson impurity models relevant for topological superconducting nanowires, providing analytical solutions for complex interactions and exploring their effects on quantum dot properties.

## Contribution

It presents a novel class of interacting Majorana-Anderson impurity models that can be solved exactly using a $ ext{Z}_2$ slave-spin approach, including models with arbitrary on-site interactions.

## Key findings

- Derived exact spectral functions for quantum dots coupled to Majorana modes.
- Analyzed how interaction strength influences quasiparticle weight and pairing.
- Explored the impact of Majorana localization length on electronic properties.

## Abstract

Motivated by recent experimental progress in the realization of hybrid structures with a topologically superconducting nanowire coupled to a quantum dot, viewed through the lens of the emerging field of correlated Majorana fermions, we introduce a class of interacting Majorana-Anderson impurity models which admit an exact solution for a wide range of parameters, including on-site repulsive interactions of arbitrary strength. The model is solved by mapping it via the $\mathbb{Z}_2$ slave-spin method to a noninteracting resonant level model for auxiliary Majorana degrees of freedom. The resulting gauge constraint is eliminated by exploiting the transformation properties of the Hamiltonian under a special local particle-hole transformation. For a spin-polarized Kitaev chain coupled to a quantum dot, we obtain exact expressions for the dot spectral functions at both zero and finite temperature. We study how the interaction strength and localization length of the end Majorana zero mode affect physical properties of the dot, such as quasiparticle weight, double occupancy, and odd-frequency pairing correlations, as well as the local electronic density of states in the superconducting chain.