Exact ground states, charge densities, and excitation energies are found using valence bond methods for N-site modified Hubbard models with uniform spacing. At the neutral-ionic transition (NIT), the ground state has a symmetry crossover in $4n$ and $4n+2$ rings with periodic and antiperiodic boundary conditions, respectively. Large site energies $\ensuremath{\Delta}$ stabilize a paired state of the half-filled chain, while large U stabilizes a covalent state. Finite-transfer integrals t shift the NIT to the covalent side of $U\ensuremath{-}2\ensuremath{\Delta}.$ Exact results to $N=16$ in the full basis and to $N=22$ in a restricted basis for large U and $\ensuremath{\Delta}$ are extrapolated to obtain the crossover and charge density of extended chains. The modified Hubbard model has a continuous NIT between a diamagnetic band insulator on the paired side and a paramagnetic Mott insulator on the covalent side. The singlet-triplet (ST), singlet-singlet (SS), and charge gaps for finite N indicate that the ST and SS gaps close at the NIT with increasing U, and that the charge gap vanishes only there. Finite-N excitations constrain all singularities to $\ifmmode\pm\else\textpm\fi{}0.1t$ of the symmetry crossover. The NIT is interpreted as a localized ground state (GS) with finite gaps on the paired side and an extended GS with vanishing ST and SS gaps on the covalent side. The charge gap and charge stiffness indicate a metallic GS at the transition that, however, is unconditionally unstable to dimerization. Finite $\ensuremath{\Delta}$ breaks electron-hole $(e\ensuremath{-}h)$ symmetry, but the modified Hubbard model has an extended $e\ensuremath{-}h$ symmetry, and a strong mixing of spin and charge excitations is limited to a few t's about the NIT. Exact finite-size results complement other approaches to valence or ferroelectric transitions in organic charge-transfer salts or in inorganic oxides, and to electron-vibration coupling and structural instabilities in one-dimensional systems.Exact ground states, charge densities, and excitation energies are found using valence bond methods for N-site modified Hubbard models with uniform spacing. At the neutral-ionic transition (NIT), the ground state has a symmetry crossover in $4n$ and $4n+2$ rings with periodic and antiperiodic boundary conditions, respectively. Large site energies $\ensuremath{\Delta}$ stabilize a paired state of the half-filled chain, while large U stabilizes a covalent state. Finite-transfer integrals t shift the NIT to the covalent side of $U\ensuremath{-}2\ensuremath{\Delta}.$ Exact results to $N=16$ in the full basis and to $N=22$ in a restricted basis for large U and $\ensuremath{\Delta}$ are extrapolated to obtain the crossover and charge density of extended chains. The modified Hubbard model has a continuous NIT between a diamagnetic band insulator on the paired side and a paramagnetic Mott insulator on the covalent side. The singlet-triplet (ST), singlet-singlet (SS), and charge gaps for finite N indicate that the ST and SS gaps close at the NIT with increasing U, and that the charge gap vanishes only there. Finite-N excitations constrain all singularities to $\ifmmode\pm\else\textpm\fi{}0.1t$ of the symmetry crossover. The NIT is interpreted as a localized ground state (GS) with finite gaps on the paired side and an extended GS with vanishing ST and SS gaps on the covalent side. The charge gap and charge stiffness indicate a metallic GS at the transition that, however, is unconditionally unstable to dimerization. Finite $\ensuremath{\Delta}$ breaks electron-hole $(e\ensuremath{-}h)$ symmetry, but the modified Hubbard model has an extended $e\ensuremath{-}h$ symmetry, and a strong mixing of spin and charge excitations is limited to a few t's about the NIT. Exact finite-size results complement other approaches to valence or ferroelectric transitions in organic charge-transfer salts or in inorganic oxides, and to electron-vibration coupling and structural instabilities in one-dimensional systems.

arXiv:cond-mat/0009153Physical review. B, Condensed matterMay 8, 200151 citations

Ground States of the Hubbard Model

Assa Auerbach

Graduate texts in contemporary physicsJan 1, 19940 citations

Soliton Energetics in Peierls-Hubbard Models

David K Campbell, Thomas DeGrand, S. Mazumdar

We study the effect of electron-electron correlations on the energetics of solitons in electron-phonon models of quasi one-dimensional materials. In these combined Peierls-Hubbard models, by use of quantum Monte Carlo techniques, we (1) establish that the ground state of an odd chain, singly charged or neutral, is a soliton; (2) calculate neutral-soliton creation energies; and (3) prove that "soliton doping" persists in the presence of correlations. We discuss the relevance of our results for trans-polyacetylene.We study the effect of electron-electron correlations on the energetics of solitons in electron-phonon models of quasi one-dimensional materials. In these combined Peierls-Hubbard models, by use of quantum Monte Carlo techniques, we (1) establish that the ground state of an odd chain, singly charged or neutral, is a soliton; (2) calculate neutral-soliton creation energies; and (3) prove that "soliton doping" persists in the presence of correlations. We discuss the relevance of our results for trans-polyacetylene.

Physical Review LettersMay 7, 1984108 citations

The Ground State Energy of the Hubbard Model in Hubbard's Approximation

Rainer J. Jelitto

Abstract We have calculated the ground state energy of the Hubbard model in the approximation of Hubbard's first paper1 . For the neutral model with nearest neighbour interaction the energy resulting from the selfconsistent paramagnetic solution is compared with those ones following from the (ferromagnetic) Hartree-Fock and an (antiferromagnetic) single particle theory. The energy of the latter one turns out to be the best approximation of the true ground state energy of the model for all values of the coupling constant V0 , but the energy derived from Hubbard's approximation, in spite of the absence of magnetic ordering, is a reasonable approximation at least for sufficiently large values of V0.Abstract We have calculated the ground state energy of the Hubbard model in the approximation of Hubbard's first paper1 . For the neutral model with nearest neighbour interaction the energy resulting from the selfconsistent paramagnetic solution is compared with those ones following from the (ferromagnetic) Hartree-Fock and an (antiferromagnetic) single particle theory. The energy of the latter one turns out to be the best approximation of the true ground state energy of the model for all values of the coupling constant V0 , but the energy derived from Hubbard's approximation, in spite of the absence of magnetic ordering, is a reasonable approximation at least for sufficiently large values of V0.

Zeitschrift für Naturforschung AJun 1, 19721 citation

The ground state of the two-dimensional Hubbard model

Yoshihiro Asai

arXiv:cond-mat/9909074Physica B Condensed MatterJun 1, 20002 citations

4n

and

4n+2

rings with periodic and antiperiodic boundary conditions, respectively. Large site energies $\ensuremath{\Delta}$ stabilize a paired state of the half-filled chain, while large U stabilizes a covalent state. Finite-transfer integrals t shift the NIT to the covalent side of $U\ensuremath{-}2\ensuremath{\Delta}.$ Exact results to

N=16

in the full basis and to

N=22

in a restricted basis for large U and $\ensuremath{\Delta}$ are extrapolated to obtain the crossover and charge density of extended chains. The modified Hubbard model has a continuous NIT between a diamagnetic band insulator on the paired side and a paramagnetic Mott insulator on the covalent side. The singlet-triplet (ST), singlet-singlet (SS), and charge gaps for finite N indicate that the ST and SS gaps close at the NIT with increasing U, and that the charge gap vanishes only there. Finite-N excitations constrain all singularities to $\ifmmode\pm\else\textpm\fi{}0.1t$ of the symmetry crossover. The NIT is interpreted as a localized ground state (GS) with finite gaps on the paired side and an extended GS with vanishing ST and SS gaps on the covalent side. The charge gap and charge stiffness indicate a metallic GS at the transition that, however, is unconditionally unstable to dimerization. Finite $\ensuremath{\Delta}$ breaks electron-hole $(e\ensuremath{-}h)$ symmetry, but the modified Hubbard model has an extended $e\ensuremath{-}h$ symmetry, and a strong mixing of spin and charge excitations is limited to a few t's about the NIT. Exact finite-size results complement other approaches to valence or ferroelectric transitions in organic charge-transfer salts or in inorganic oxides, and to electron-vibration coupling and structural instabilities in one-dimensional systems.