# Analytical approach to the Bose polaron problem in one dimension

## TL;DR

This paper presents an analytical method to study the ground state properties of a one-dimensional Bose polaron system, validated against quantum Monte Carlo and numerical results, offering a new tool for strongly interacting impurity problems.

## Contribution

The paper introduces a novel analytical formalism for calculating zero-temperature properties of 1D Bose polarons with weak to moderate interactions, validated by numerical methods.

## Key findings

- Analytical expressions match quantum Monte Carlo results.
- Method effectively describes finite size systems.
- Provides a simple tool for strongly interacting impurity studies.

## Abstract

We discuss the ground state properties of a one-dimensional bosonic system doped with an impurity (the so-called Bose polaron problem). We introduce a formalism that allows us to calculate analytically the thermodynamic zero-temperature properties of this system with weak and moderate boson-boson interaction strengths for any boson-impurity interaction. Our approach is validated by comparing to exact quantum Monte Carlo calculations. In addition, we test the method in finite size systems using numerical results based upon the similarity renormalization group. We argue that the introduced approach provides a simple analytical tool for studies of strongly interacting impurity problems in one dimension.