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

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 a mixture with up to ten majority fermions.

Automated summary

A method for numerically exact calculation is proposed in this article for a mixture with a single impurity and several majority fermions in a harmonic potential. The method separates one degree of freedom through a tailored canonical transformation and performs exact diagonalization on the simplified Hamiltonian. This method is particularly effective for heavy impurities.