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A systematic interpolatory method for an impurity in a one-dimensional fermionic background

Erik J. Lindgren, Rafael E. Barfknecht, Nikolaj T. Zinner

SciPost Phys. 9, 005 (2020) · published 13 July 2020


We explore a new numerical method for studying one-dimensional quantum systems in a trapping potential. We focus on the setup of an impurity in a fermionic background, where a single distinguishable particle interacts through a contact potential with a number of identical fermions. We can accurately describe this system, for various particle numbers, different trapping potentials and arbitrary finite repulsion, by constructing a truncated basis containing states at both zero and infinite repulsion. The results are compared with matrix product states methods and with the analytical result for two particles in a harmonic well.

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