Recently, nonuniqueness of external electrostatic and magnetic fields yielding a given many-electron ground state has been pointed out [K. Capelle and G. Vignale, Phys. Rev. Lett. 86, 5546 (2001); H. Eschrig and W. E. Pickett, Solid State Commun. 118, 123 (2001)], implying the nondifferentiability of the ground-state energy functional of spin-density-functional theory (SDFT), on the basis of which the applicability of widely used DFT methods in SDFT has been put into question and the need for a critical reexamination of those applications has been concluded. Here it is shown, for collinear magnetic fields, that the nonuniqueness of the external potentials in SDFT does not imply the nonexistence of number-conserving functional derivatives as well, with the use of which therefore problems arising from the nondifferentiability are avoided.
We study the ground-state properties of two-dimensional quantum spin systems having the valence-bond-solid (VBS) type ground states. The `product-of-tensors' form of the ground-state wavefunction of the system is utilized to associate it with an equivalent classical lattice statistical model which can be treated by the transfer-matrix method. For diagonalization of the transfer matrix, we employ the product-wavefunction renormalization group method, which is a variant of the density-matrix renormalization group method. We obtain the correlation length and the sublattice magnetization accurately. For the anisotropically `deformed' S = 3/2 VBS model on the honeycomb lattice, we find that the correlation length as a function of the deformation parameter behaves very much as that in the S = 3/2 VBS chain.
Description of many-electron systems with a fractional electron number
Ntot and fractional spin
Mtot is of great importance in physical chemistry, solid state physics and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system, and characterize the dependence of the energy and the spin-densities on both
Ntot and
Mtot, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at constant
Ntot, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.