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Physical Review Letters

Exact results for a Hubbard chain with long-range hopping

Florian Gebhard, Andrei E. Ruckenstein

Published Jan 13, 1992• 94 citations
Publisher

Abstract

We give the exact spectrum and thermodynamics for a long-range hopping Hubbard chain with linear dispersion. This model exhibits a Mott-Hubbard metal-insulator transition at half filling when the interaction strength U equals the bandwidth W. The solution for U\ensuremath{\gg}W also covers the corresponding t-J model, which reduces to the spin model of Haldane and Shastry at half filling. We mention possible extensions of the model in one and higher dimensions.

DOI
10.1103/physrevlett.68.244

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We study the ground-state phase diagram of the Anderson-Hubbard model with correlated hopping at half-filling in one dimension. The Hamiltonian has a local Coulomb repulsion UUU and a disorder potential with local energies randomly distributed in the interval $(\ensuremath{-}W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites has the same amplitude ttt. We identify three different phases as functions of the disorder amplitude WWW and Coulomb interaction strength U>0U>0U>0. When U<4tU<4tU<4t the system shows a metallic phase: (i) only when no disorder is present W=0W=0W=0 or an Anderson-localized phase, (ii) when disorder is introduced $W\ensuremath{\ne}0$. When U>4tU>4tU>4t the Anderson-localized phase survives as long as disorder effects dominate on the interaction effects, otherwise a Mott-insulator phase (iii) arises. Phases (i) and (ii) are characterized by a finite density of doublons and a vanishing charge gap among the ground state and the excited states. Phase (iii) is characterized by the vanishing density of doublons and a finite gap for the charge excitations.