Ground-state energy and density response of a one-dimensional fermion system with repulsiveδ-function interaction

The ground-state energy of a one-dimensional fermion system interacting via a repulsive $\delta$-function potential is calculated rigorously within the "ladder" approximation as a function of the coupling constant and the results compared with those given by the exact solution of Yang. Comparison with other many-body approximate theories has also been made. The density-density response function has also been calculated in an approximation in which the particle-hole interaction in the polarization bubble is taken into account to all orders. Results of this dynamic theory are compared with those of other approximations.