Numerical studies on critical states in two-dimensions and correlated electrons in low dimensions

Yasuhiro Hatsugai

Yasuhiro Hatsugai

Pinaki Sengupta

E. Räsänen, Stefano Pittalis, Klaus Capelle +1 more

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.

N. H. March

Many-body effects in jellium, M.P. Tosi solids with weak and strong electron correlations, P. Fulde ground and low-lying excited states of interacting electron systems - a survey and some critical analyses, B. Farid failure of Fermi liquid theory in two and three dimensions, G. Baskaran quantum phase transitions in electronic systems, T.R. Kirkpatrick and D. Belitz density matrices, density functional theory and quantum Monte Carlo calculations, N.H. March.

S. V. Kravchenko