Many-body effects in the one-dimensional electron gas with short-range interaction

We discuss interaction effects for the one-dimensional electron gas with a repulsive delta-function interaction potential by using the random-phase approximation and a local-field correction. Analytical results for the local-field correction of charge-density fluctuations and spin-density fluctuations are obtained. The ground-state energy is found to be in better agreement with the exact result than the ground-state energy calculated within the random-phase approximation. We calculate the pair-correlation functions for electron with parallel and antiparallel spins and the paramagnetic susceptibility. The energies of the collective density modes omega(d)(q) and the collective spin modes omega(s)(q) are calculated and compared with the energy of the electron-hole excitations omega(eh+/-)(q): omega(d)(q-->0)>omega(eh+/-)(q-->0) >omega(s)(q-->0). The critical exponents for the long-distance behavior of correlation functions are found to be described by local-field corrections. We compare our results for the critical exponents with recent results obtained by bosonization techniques and the conformal field theory.