A theorem about the spin properties of the ground state and the ordering of the energy levels for different spins of an interacting-electron model including an arbitrary diagonal interacting potential, an antiferromagnetic exchange, and an electron pair-hopping term for particles on a one-dimensional lattice is stated and proved. We show that when the number of electrons N=4n+2 (n an integer) with periodic boundary conditions or N=4n with antiperiodic boundary conditions, the ground state is a nondegenerate singlet. This theorem generalizes a similar theorem Lieb and Mattis proved for the one-dimensional interacting electron system.A theorem about the spin properties of the ground state and the ordering of the energy levels for different spins of an interacting-electron model including an arbitrary diagonal interacting potential, an antiferromagnetic exchange, and an electron pair-hopping term for particles on a one-dimensional lattice is stated and proved. We show that when the number of electrons N=4n+2 (n an integer) with periodic boundary conditions or N=4n with antiperiodic boundary conditions, the ground state is a nondegenerate singlet. This theorem generalizes a similar theorem Lieb and Mattis proved for the one-dimensional interacting electron system.

Physical review. B, Condensed matterNov 1, 19928 citations

THEOREM ON THE ONE-DIMENSIONAL INTERACTING-ELECTRON SYSTEM ON A LATTICE

No author provided

A theorem about the spin properties of the ground state and the ordering of the energy levels for different spins of an interacting-electron model including an arbitrary diagonal interacting potential, an antiferromagnetic exchange, and an electron pair-hopping term for particles on a one-dimensional lattice is stated and proved. We show that when the number of electrons N = 4n + 2 (n an integer) with periodic boundary conditions or N = 4n with antiperiodic boundary conditions, the ground state is a nondegenerate singlet. This theorem generalizes a similar theorem Lieb and Mattis proved for the one-dimensional interacting electron system.A theorem about the spin properties of the ground state and the ordering of the energy levels for different spins of an interacting-electron model including an arbitrary diagonal interacting potential, an antiferromagnetic exchange, and an electron pair-hopping term for particles on a one-dimensional lattice is stated and proved. We show that when the number of electrons N = 4n + 2 (n an integer) with periodic boundary conditions or N = 4n with antiperiodic boundary conditions, the ground state is a nondegenerate singlet. This theorem generalizes a similar theorem Lieb and Mattis proved for the one-dimensional interacting electron system.

Sep 10, 20260 citations

Ground state properties of a laterally confined two-dimensional electron gas

Lucia Dandrea, Francesco Pederiva, E. Lipparini

We present an accurate diffusion Monte Carlo computation of the ground state of a two-dimensional electron gas laterally confined by a harmonic potential in the effective mass-dielectric constant approximation. The computation is made explicitly including the second dimension, and can therefore address the occurrence of phase transitions in the system. The system was studied as a function of the one-dimensional Wigner-Seitz parameter ${r}_{s}=1/2{\ensuremath{\rho}}^{1\text{D}}$ in the range $0.5\ensuremath{\le}{r}_{s}\ensuremath{\le}7$. The ground state is found to be spin polarized for ${r}_{s}>3$ .We present an accurate diffusion Monte Carlo computation of the ground state of a two-dimensional electron gas laterally confined by a harmonic potential in the effective mass-dielectric constant approximation. The computation is made explicitly including the second dimension, and can therefore address the occurrence of phase transitions in the system. The system was studied as a function of the one-dimensional Wigner-Seitz parameter ${r}_{s}=1/2{\ensuremath{\rho}}^{1\text{D}}$ in the range $0.5\ensuremath{\le}{r}_{s}\ensuremath{\le}7$. The ground state is found to be spin polarized for ${r}_{s}>3$.

Physical Review BApr 27, 20090 citations

Disorder and Interactions in the System of Quasi One-dimensional Electrons

L. P. Gor’kov

Modern problems in condensed matter sciencesJan 1, 19852 citations

{r}_{s}>3