# Systematic interpolatory ansatz for one-dimensional polaron systems

## TL;DR

This paper introduces a new variational approach using a truncated basis to accurately study one-dimensional Fermi polaron systems at any interaction strength, improving computational efficiency and accuracy.

## Contribution

The authors develop a systematic interpolatory ansatz that combines zero and infinite repulsion states for better modeling of 1D polaron systems.

## Key findings

- Accurately describes polaron energies, densities, and correlations at finite interactions.
- Validates the method against matrix product states and analytical solutions.
- Applicable to various trapping potentials and particle numbers.

## Abstract

We explore a new variational principle for studying one-dimensional quantum systems in a trapping potential. We focus on the Fermi polaron problem, where a single distinguishable impurity interacts through a contact potential with a background of identical fermions. We can accurately describe this system at arbitrary finite repulsion by constructing a truncated basis containing states at both the limits of zero and infinite repulsion. We show how to construct this basis and how to obtain energies, density matrices and correlation functions, and provide results both for a harmonic well and a double well for various particle numbers. The results are compared both with matrix product states methods and with the analytical result for two particles in a harmonic well.