Computational Study of Correlated Electrons in One-Dimension

Enrico Arrigoni

Nelson Oyindenyifa Nenuwe

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.

Alexander F. Kemper

Girish S. Setlur

The degenerate Fermi gas coupled to a random potential is used to study metal-insulator transitions in various dimensions. We first recast the problem in the sea-boson language that allows for an easy evaluation of important physical attributes. We evaluate the dynamical number-number correlation function and from this compute the a.c. conductivity. We find that the d.c. conductivity vanishes in one and two dimensions. For a hamiltonian that forbids scattering of an electron from within the Fermi surface to another state within the Fermi surface we find that there is no metal-insulator transition in three dimensions either.

Frédéric Lesage, Hubert Saleur

We show how the form-factors approach can be used to compute correlators of operators with non-trivial anomalous dimension in quantum impurity problems. This is done by a series of regularizations that cure completely the infrared divergencies, without spoiling the exactedness of the method. As an application, we compute for the `Friedel oscillations' of charge density induced by a single impurity in a one-dimensional Luttinger liquid of spinless electrons.