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arXiv:cond-mat/9510033 · Physical Review Letters

Anomalous Flux Quantization in a Hubbard Ring with Correlated Hopping

Liliana Arrachea, Armando A. Aligia, Eduardo R. Gagliano

Published Jun 3, 1996• 53 citations
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Abstract

We solve exactly a generalized Hubbard ring with twisted boundary conditions. The magnitude of the nearest-neighbor hopping depends on the occupations of the sites involved and the term which modifies the number of doubly occupied sites ${t}_{\mathrm{AB}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. Although $\ensuremath{\eta}$-pairing states with off-diagonal long-range order are part of the degenerate ground state, the behavior of the energy as a function of the twist rules out superconductivity in this limit. A small ${t}_{\mathrm{AB}}$ breaks the degeneracy and for moderate repulsive $U$ introduce superconducting correlations which lead to ``anomalous'' flux quantization.

DOI
10.1103/physrevlett.76.4396

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Using numerical diagonalization of a $4\ifmmode\times\else\texttimes\fi{}4$ cluster, we calculate on-site s, extended-s,s,s, and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing correlation functions (PCF's) in an effective generalized Hubbard model for the cuprates, with nearest-neighbor correlated hopping and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}.$ The vertex contributions to the PCF's are significantly enhanced, relative to the ${t\ensuremath{-}t}^{\ensuremath{'}}\ensuremath{-}U$ model. The behavior of the PCF's and their vertex contributions, and signatures of anomalous flux quantization, indicate superconductivity in the d-wave channel for moderate doping and in the s-wave channel for high doping and small U.
We consider an extended one-dimensional Hubbard model in which the magnitude of the hopping between two sites for particles with given spin depends on the occupation of the states with opposite spin at both sites. Diagonalizing exactly finite-size chains, and using known results of conformal field theory we delimit the regions of parameters for which two particles bind and the pair superconducting correlation functions are the dominant ones at large distances. For Coulomb repulsion U smaller than a critical density-dependent value Uc{\mathit{U}}_{\mathit{c}}Uc​ and any density, there are ranges of the ratios of the hopping parameters for which the superconducting fluctuations dominate. At half filling, for parameters within this range, a transition from a regime with dominant superconducting correlations to an insulating state takes place as a function of U. We also study the model for parameters near a recently found exactly solvable limit in which the number of doubly occupied sites is conserved.
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.
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We present stochastic diagonalization results for the ground-state energy and the largest eigenvalue of the two-fermion density matrix of the BCS reduced Hamiltonian, the Hubbard model, and the Hubbard model with correlated hopping. The system-size dependence of this eigenvalue is used to study the existence of Off-Diagonal Long-Range Order in these models. We show that the model with correlated hopping and repulsive on-site interaction can exhibit Off-Diagonal Long-Range Order. Analytical results for some special limiting cases indicate that Off-Diagonal Long-Range Order not always implies superconductivity.