  Electronic structure calculations are routinely carried out within the
framework of density-functional theory, often with great success. For electrons
in reduced dimensions, however, there is still a need for better approximations
to the exchange-correlation energy functional. Furthermore, the need for
properly describing current-carrying states represents an additional challenge
for the development of approximate functionals. In order to make progress along
these directions, we show that simple and efficient expressions for the
exchange energy can be obtained by considering the short-range behavior of the
one-body spin-density matrix. Applications to several two-dimensional systems
confirm the excellent performance of the derived approximations, and verify the
gauge-invariance requirement to be of great importance for dealing with
current-carrying states.
