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arXiv:0706.0331 · Journal of Physics Condensed Matter

Extended Hubbard model on a C20molecule

Fei Lin, Erik Schwartz Sørensen, Catherine Kallin, A. J. Berlinsky

Published Oct 11, 2007• 8 citations
arXivHTMLPDF

Abstract

The electronic correlations on a C 20 molecule, as described by an extended Hubbard Hamiltonian with a nearest-neighbor Coulomb interaction of strength V , are studied using quantum Monte Carlo and exact diagonalization methods. For electron-doped C 20 , it is known that pair binding arising from a purely electronic mechanism is absent within the standard Hubbard model ( V = 0). Here we show that this is also the case for hole doping for 0< U / t ≤3 and that, for both electron and hole doping, the effect of a non-zero V is to work against pair binding. We also study the magnetic properties of the neutral molecule, and find transitions between spin singlet and triplet ground states for either fixed U or V values. In addition, spin, charge and pairing correlation functions on C 20 are computed. The spin–spin and charge–charge correlations are very short-range, although a weak enhancement in the pairing correlation is observed for a distance equal to the molecular diameter.

DOI
10.1088/0953-8984/19/45/456206

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The electronic correlations on a C 20 molecule, as described by an extended Hubbard Hamiltonian with a nearest-neighbor Coulomb interaction of strength V , are studied using quantum Monte Carlo and exact diagonalization methods. For electron-doped C 20 , it is known that pair binding arising from a purely electronic mechanism is absent within the standard Hubbard model ( V = 0). Here we show that this is also the case for hole doping for 0< U / t ≤3 and that, for both electron and hole doping, the effect of a non-zero V is to work against pair binding. We also study the magnetic properties of the neutral molecule, and find transitions between spin singlet and triplet ground states for either fixed U or V values. In addition, spin, charge and pairing correlation functions on C 20 are computed. The spin–spin and charge–charge correlations are very short-range, although a weak enhancement in the pairing correlation is observed for a distance equal to the molecular diameter.
To clarify the effects of next-nearest-neighbor electron hopping ${t}^{\ensuremath{'}}$ on the spin, charge, and pairing correlations, we studied the two-dimensional $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}U$ Hubbard model using the constrained-path Monte Carlo technique. We found that a negative ${t}^{\ensuremath{'}}$ suppresses the spin fluctuations near the Brillouin zone point $M=(\ensuremath{\pi},\ensuremath{\pi})$ and the charge fluctuations near the point $X=(\ensuremath{\pi},0),$ while a positive ${t}^{\ensuremath{'}}$ has the opposite effect. For a negative ${t}^{\ensuremath{'}},$ we also found that the long-range vertex contributions to the pairing correlations are heavily suppressed, but the local contributions are enhanced. Over the entire hole doping range studied, the d-wave long-range vertex contributions to pairing dominated those of the extended s-wave vertex contributions. In general, we did not find any tendency for these correlations to grow with increasing system size. We also did a limited number of simulations with an attractive nearest neighbor density-density interaction added to the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}U$ model. It enhanced the long-range vertex contributions to the pairing correlations only for weak values of U.
The single-band Hubbard model (both with and without first-neighbor interactions) is studied by exact diagonalization on several one- and two-dimensional clusters, ranging from four to nine sites, including rings and arrangements of squares. Occupancies include the half-filled band (one electron per site) and configurations with one and two holes in the half-filled band. Ground-state properties are determined for a wide range of parameters. We discuss the phase diagram in the (U,V) plane and consider spin, charge, and pairing correlations. The binding of a pair of holes is investigated. Circumstances in which binding and pairing are enhanced by first-neighbor interactions are described.
We simulated the three-band Hubbard model using the constrained-path Monte Carlo (CPMC) method in search for a possible superconducting ground state. The CPMC is a ground-state method that is free of the exponential scaling of computing time with system size. We calculated the binding energy of a pair of holes for systems up to $6\ifmmode\times\else\texttimes\fi{}4$ unit cells. We also studied the pairing correlation functions versus distance for both the ddd-wave and extended sss-wave channels in systems up to $6\ifmmode\times\else\texttimes\fi{}6$. We found that holes bind for a wide range of parameters and that the binding increased as the system size is increased. However, the pairing correlation functions decay quickly with distance. For the extended sss channel, we found that as the Coulomb interaction Ud{U}_{d}Ud​ on the Cu sites is increased, the long-range part of the correlation functions is suppressed and fluctuates around zero. For the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ channel, we found that the correlations decay rapidly with distance towards a small positive value. However, this value becomes smaller as the interaction Ud{U}_{d}Ud​ or the system size is increased.
Using the constrained path Monte Carlo method, we simulated the two-dimensional, three-band Hubbard model to study pairing, charge, and spin correlations as a function of electron and hole doping and the Coulomb repulsion Vpd{V}_{\mathrm{pd}}Vpd​ between charges on neighboring Cu and O lattice sites. As a function of distance, both the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave and extended s-wave pairing correlations decayed quickly. In the charge-transfer regime, increasing Vpd{V}_{\mathrm{pd}}Vpd​ decreased the long-range part of the correlation functions in both channels, while in the mixed-valent regime, it increased the long-range part of the s-wave behavior but decreased that of the d-wave behavior. Still the d-wave behavior dominated. At a given doping, increasing Vpd{V}_{\mathrm{pd}}Vpd​ increased the spin-spin correlations in the charge-transfer regime but decreased them in the mixed-valent regime. Also, increasing Vpd{V}_{\mathrm{pd}}Vpd​ suppressed the charge-charge correlations between neighboring Cu and O sites. Electron and hole doping away from half-filling was accompanied by a rapid suppression of antiferromagnetic correlations. Our results suggest that adding a repulsive Vpd{V}_{\mathrm{pd}}Vpd​ to the model does not enhance its tendency toward superconductivity even though the behavior of the spin structure factor is consistent with the properties of some high-temperature superconducting materials.
In this study we have computed the pair correlation functions in the two-dimensional Hubbard model using a quantum Monte Carlo method. We employ a new diagonalization algorithm in the quantum Monte Carlo method which is free from the negative sign problem. We show that the d-wave pairing correlation function is indeed enhanced slightly for the positive on-site Coulomb interaction U when doping away from the half-filling. When the system size becomes large, the pair correlation function P d increases for U > 0 compared to the non-interacting case, while P d is suppressed for U > 0 when the system size is small. The enhancement ratio P d [ U ]/ P d [ U = 0] will give a criterion on the existence of superconductivity. The ratio P d [ U ]/ P d [ U = 0] increases almost linearly ∝ L when the system size L × L is increased. This increase is a good indication of the existence of a superconducting phase in the two-dimensional Hubbard model. There is, however, no enhancement of pair correlation functions in the half-filled case, which indicates the absence of superconductivity without hole doping.
We investigate the binding of holes and the emergence of competing spin-charge order in the simple and extended Hubbard model using exact diagonalization on the 3x4 cylindrical lattice. For the simple Hubbard model (V=0), we find weakly bound hole pairing mediated by magnetic correlations at intermediate repulsive U, without any evidence of phase separation. Introducing nearest-neighbor interaction V reveals a rich phase diagram: attractive V drives multi-hole clustering and phase separation with localized magnetic quenching, while repulsive V stabilizes charge-density-wave (CDW) order that coexists with bound hole pairs within a modulated magnetic background. At strong coupling (U=10), the competition sharpens, with attractive V overcoming on-site repulsion to form magnetically quenched clusters and repulsive V producing robust CDW order that constrains pairing. Real-space analysis of spin and charge correlations provides microscopic evidence of distinct binding mechanisms -- phase separation versus correlation-mediated pairing -- depending on the sign and strength of intersite interaction V . Our results establish a comprehensive picture of how nonlocal Coulomb interactions reshape the landscape of hole-binding and collective order in correlated electron systems.