We investigate the ground state of the Kondo-Hubbard model employing the recently introduced idea of spin-reflection positivity. It is shown exactly that the Kondo-Hubbard model for $J<0$ and $U>|J|/4$ at half filling has a unique ground state which can be ferromagnetic or singlet according to the lattice structure. In particular, for the Kondo lattice with $U>|J|/4$ , the ground state is a singlet. We also show a theorem for the Kondo-Hubbard model with the anisotropic antiferromagnetic coupling ${J}_{\ensuremath{\perp}}>0$ and ${J}_{z}\ensuremath{\le}0$ for $U>|{J}_{z}|/4$ .We investigate the ground state of the Kondo-Hubbard model employing the recently introduced idea of spin-reflection positivity. It is shown exactly that the Kondo-Hubbard model for $J<0$ and $U>|J|/4$ at half filling has a unique ground state which can be ferromagnetic or singlet according to the lattice structure. In particular, for the Kondo lattice with $U>|J|/4$, the ground state is a singlet. We also show a theorem for the Kondo-Hubbard model with the anisotropic antiferromagnetic coupling ${J}_{\ensuremath{\perp}}>0$ and ${J}_{z}\ensuremath{\le}0$ for $U>|{J}_{z}|/4$.

Physical Review LettersJun 12, 199532 citations

The ground state of the Hubbard model

E. O. Aiyohuyin, A. A. Oni-Ojo

Journal of the Nigerian Association of Mathematical PhysicsJun 13, 20080 citations

Hartree theory for the negative- U extended Hubbard model: Ground state

S. Robaszkiewicz, R. Micnas, K. A. Chao

We have investigated the ground-state properties of the negative- $U$ extended Hubbard model in the weak-coupling regime with the Hartree theory formulated in terms of the Bogoliubov variational approach. While the pure phases of charge order (CO), singlet superconducting (SS), and nonordered can be solved analytically with a model density of states, the mixed phase of CO and SS requires numerical computation. The ground-state phase diagram is derived, and the order parameters and the chemical potential of the ground state are analyzed. The characteristic difference between the behaviors of the SS and the CO order parameters at very weak coupling suggests a complicated competition between various interactions. Present results are compared with those derived earlier for the strong-coupling regime.We have investigated the ground-state properties of the negative-$U$ extended Hubbard model in the weak-coupling regime with the Hartree theory formulated in terms of the Bogoliubov variational approach. While the pure phases of charge order (CO), singlet superconducting (SS), and nonordered can be solved analytically with a model density of states, the mixed phase of CO and SS requires numerical computation. The ground-state phase diagram is derived, and the order parameters and the chemical potential of the ground state are analyzed. The characteristic difference between the behaviors of the SS and the CO order parameters at very weak coupling suggests a complicated competition between various interactions. Present results are compared with those derived earlier for the strong-coupling regime.

Physical review. B, Condensed matterOct 1, 198164 citations

Ground States of the Hubbard Model

Assa Auerbach

Graduate texts in contemporary physicsJan 1, 19940 citations

Symmetry crossover and excitation thresholds at the neutral-ionic transition of the modified Hubbard model

Y. Anusooya Pati, Z. G. Soos, Anna Painelli

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

We investigate the ground state of the Kondo-Hubbard model employing the recently introduced idea of spin-reflection positivity. It is shown exactly that the Kondo-Hubbard model for

J<0

and

U>|J|/4

at half filling has a unique ground state which can be ferromagnetic or singlet according to the lattice structure. In particular, for the Kondo lattice with

U>|J|/4

, the ground state is a singlet. We also show a theorem for the Kondo-Hubbard model with the anisotropic antiferromagnetic coupling ${J}_{\ensuremath{\perp}}>0$ and ${J}_{z}\ensuremath{\le}0$ for

U>|{J}_{z}|/4

We have investigated the ground-state properties of the negative-

U

extended Hubbard model in the weak-coupling regime with the Hartree theory formulated in terms of the Bogoliubov variational approach. While the pure phases of charge order (CO), singlet superconducting (SS), and nonordered can be solved analytically with a model density of states, the mixed phase of CO and SS requires numerical computation. The ground-state phase diagram is derived, and the order parameters and the chemical potential of the ground state are analyzed. The characteristic difference between the behaviors of the SS and the CO order parameters at very weak coupling suggests a complicated competition between various interactions. Present results are compared with those derived earlier for the strong-coupling regime.

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.