An Exactly Soluble Model of a Many-Fermion System

TLDR

The paper studies an exactly solvable one‑dimensional many‑fermion model with realistic pair interactions and examines its response to external fields. The authors compute the exact ground‑state momentum distribution analytically. The exact solution reveals a continuous momentum distribution with infinite slope at the Fermi surface, and perturbation theory yields qualitatively similar behavior.

Abstract

An exactly soluble model of a one-dimensional many-fermion system is discussed. The model has a fairly realistic interaction between pairs of fermions. An exact calculation of the momentum distribution in the ground state is given. It is shown that there is no discontinuity in the momentum distribution in this model at the Fermi surface, but that the momentum distribution has infinite slope there. Comparison with the results of perturbation theory for the same model is also presented, and it is shown that, for this case at least, the perturbation and exact answers behave qualitatively alike. Finally, the response of the system to external fields is also discussed.