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International Journal of Modern Physics B

MOTT TRANSITION IN AN EXACTLY SOLVABLE K.S.S.H. MODEL

Arianna Montorsi, Mario Rasetti

Published Apr 1, 1991• 6 citations
Publisher

Abstract

The solution of the K.S.S.H.-like model shown to be exactly solvable in any number of dimensions, for a particular choice of the coupling constant describing the hopping process amplitude, both for finite size and in the thermodynamic limit, is discussed in detail. The analysis of the zero-temperature phase space in d = 2 shows that the model exhibits a transition in the number of doubly occupied sites order parameter, which at half-filling coincides with the Mott transition found for the Hubbard model in the Gutzwiller approximation.

DOI
10.1142/s0217979291000511

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The solution of the K.S.S.H.-like model shown to be exactly solvable in any number of dimensions, for a particular choice of the coupling constant describing the hopping process amplitude, both for finite size and in the thermodynamic limit, is discussed in detail. The analysis of the zero-temperature phase space in d = 2 shows that the model exhibits a transition in the number of doubly occupied sites order parameter, which at half-filling coincides with the Mott transition found for the Hubbard model in the Gutzwiller approximation.
A solvable model of d = 1 spinless fermions at half-filling which exhibits a Mott transition is studied in detail. Many response functions are computed: at zero and nonzero temperatures, in the insulating and metallic sites, at the transition, and at q ≃ 0, 2k F . Some quantities are computed exactly, others only upto a scale factor. Some results are old, but mentioned here for completeness. Some are rederived using new tools such as conformal invariance. The rest are new. Next, the effect of randomness on the Mott state is explored. It is found, on the basis of Imry-Ma type arguments that no matter how large the gap is, the Mott insulator turns into an Anderson insulator immediately.
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.
We study a generalized Hubbard model with on-site interaction U, nearest-neighbor repulsion V, and general correlated hopping under the condition that the number of doubly occupied sites is conserved. We find the exact ground state (GS) in arbitrary dimension in two wide regions of parameters. In one of them the GS is a Mott insulator (MI) and in the other it is a charge-density wave (CDW). The boundary of the MI and a large part of that of the CDW are determined exactly for relevant lattices. We study numerically the effect of relaxing the above-mentioned condition.
We obtain the exact solution of a general Hubbard chain with kinetic energy ttt, bond-charge interaction XXX and on-site interaction UUU with the only restriction t=Xt = Xt=X. At zero temperature and half filling, the model exhibits a Mott transition at U=4tU = 4tU=4t. In the metallic phase and near half filling, superconducting states are part of the degenerate ground state and are favored for small UUU if the system is slightly perturbed.