Current density functional theory in a continuum and lattice lagrangians: Application to spontaneously broken chiral ground states

Abstract

We formulate the current-density functional theory for systems in arbitrarily strong magnetic fields. A set of self-consistent equations comparable to the Kohn–Sham equations for ordinary density functional theory is derived, and proved to be gauge-invariant and to satisfy the continuity equation. These equations of Vignale and Rasolt involve the gauge field corresponding to the external magnetic field as well as a new gauge field generated entirely from the many-body interactions. We next extend this gauge theory (following Rasolt and Vignale) to a lattice Lagrangian believed to be appropriate to a tight-binding Hamiltonian in the presence of an external magnetic field. We finally examine the nature of the ground state of a strongly nonuniform electron gas in the presence of this many-body, self-induced gauge field. © 1992 John Wiley & Sons, Inc.