Several fermions strongly interacting with a heavy mobile impurity in a one-dimensional harmonic trap

TL;DR

This paper introduces a numerically exact method for analyzing a few-fermion mixture with a heavy impurity in a one-dimensional harmonic trap, enabling precise calculations of energy and density profiles.

Contribution

The authors develop a tailored canonical transformation and exact diagonalization technique that outperforms standard methods for heavy impurities in one-dimensional fermionic systems.

Findings

Accurate energy and density profiles for up to ten fermions with a heavy impurity.

Method is especially effective for heavy impurities, surpassing traditional exact diagonalization.

Provides a new computational tool for few-body quantum systems in harmonic traps.

Abstract

We propose a numerically exact method for a mixture with a single impurity immersed in several majority fermions, confined in a harmonic potential. We separate one of the degrees of freedom through an appropriately tailored canonical transformation and perform exact diagonalization on the simplified Hamiltonian. This method is especially effective for a heavy impurity, where it outmatches the typical exact diagonalization approach. We used our method to calculate energy and density profiles of the first few eigenstates for the mixture with up to ten majority fermions.