Time-dependent variational principle and the effective action in density-functional theory and Berry’s phase

An alternative form of the variational principle is set up by defining an action functional which takes explicit account of the time path and thus is different from that used traditionally in time-dependent density-functional theory. This has the attractive feature of not having the formal difficulties in defining the effective potential and the effective interaction as its functional derivatives. Also, the Berry phase, not explicitly found at first sight in a time-dependent density-functional theory, is shown to reside in this action functional. It lies buried as the sum over the individual phases of the occupied states associated with the time-dependent Kohn-Sham orbitals. Some recent work on superconductivity and ferroelectricity in the literature are cited as examples of the Berry-phase considerations developed here. © 1996 The American Physical Society.