Free correlation energy of unpolarized and fully spin-polarized electron quantum wire

We have numerically calculated the free correlation energy fc of an electron quantum wire for two completely different electronic spin-states i.e. the unpolarized and fully polarized states. The dynamics of electron (spin) correlations is included through the dynamic/quantum version of Singwi, Tosi, Land and Sjolander (the so called qSTLS) mean-field approximation. The results for fc are reported for both the electron spin-states over a wide range of temperature and linear electron number density. Ata fixed temperature, the magnitude of fcin unpolarized state is found to be always more thanthat of the fully-polarized spin-state. To highlight the effect of dynamics of electron correlations, our results of fc are compared withthe (static) STLS theory. We note that the magnitude of the STLS fc is small in comparison to the qSTLS results and the difference between them is quite significant at low electronnumber density.