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

Abstract

The ground-state energy of a one-dimensional fermion system interacting Uia a repulsive 5-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.

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

“…G(␥) is the LFC for density fluctuations, and was discussed before. 5,19 Collective modes are defined by poles of the response functions: 1/X"q, d (q)…ϭ0 describes the collective modes d (q) for density (d) excitations ͑zero sound͒. Within the STLS approach, the LFC is given by 5…”

“…2 for g v ϭ1 as the dashed line. Numerical results for this model within the ladder approximation 19 are shown by the solid line. The groundstate energy calculated within the ladder approximation is very near to the exact result.…”

“…19 for density modes. Note that B Ϯ (q)ϭ1Ϯ͉q͉/2k F describes the electron-hole ͑eh͒ spectrum via Ϯeh /⑀ F ϭ2͉q͉͉B Ϯ (q)͉/k F .…”

“…In the STLS approach the frequency dependence is neglected, and it was shown that G STLS (q)ϭG(q,→ϱ). 19 One motivation for the present paper was ͑i͒ to obtain analytical results which can be used by experimenters to estimate the importance of many-body effects, and ͑ii͒ to test the analytical form of the SSF. Our results concerning the valley degeneracy represent a generalization of the STLS and LST approaches.…”

Correlations in a one-dimensional Bose gas

“…Such an approach was shown to work quite well for 1D fermions interacting with a ␦ function. 24 In summary, we have considered the correlation effects in a system of 1D bosons interaction with a short-range potential. We have introduced a local-field factor based on the Vashishta-Singwi approach to describe the correlation effects.…”