Reactive Hall constant of strongly correlated electrons

The zero-temperature Hall response within tight-binding models of correlated electrons is studied. Using the linear response theory and a linearization in the magnetic field B, a general relation for the reactive (zero-frequency) Hall constant R-H(0) in the fast (transport) limit is derived, involving only matrix elements between the lowest excited states at B=0; for noninteracting fermions, the Boltzmann expression is reproduced. For a Fermi liquid with a well defined Fermi surface and linear gapless excitations an analogous expression is found more generally. In the specific case of quasi-one-dimensional correlated systems, a relation of R-H(0) to the charge stiffness D is recovered. A similar analysis is performed and discussed for D and the compressibility.