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Physical review. B, Condensed matter

Quantum Monte Carlo study of Spin, Charge, and Pairing correlations in the t−t′−U Hubbard model

Zhongbing Huang, Hua Lin, James E. Gubernatis

Published Oct 18, 2001• 49 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.64.205101

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To clarify the effects of next-nearest-neighbor electron hopping t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ on the spin, charge, and pairing correlations, we studied the two-dimensional t\ensuremath−t\ensuremath′\ensuremath−Ut\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}Ut\ensuremath−t\ensuremath′\ensuremath−U Hubbard model using the constrained-path Monte Carlo technique. We found that a negative t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ suppresses the spin fluctuations near the Brillouin zone point M=(\ensuremathπ,\ensuremathπ)M=(\ensuremath{\pi},\ensuremath{\pi})M=(\ensuremathπ,\ensuremathπ) and the charge fluctuations near the point X=(\ensuremathπ,0),X=(\ensuremath{\pi},0),X=(\ensuremathπ,0), while a positive t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ has the opposite effect. For a negative t\ensuremath′,{t}^{\ensuremath{'}},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−Ut\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}Ut\ensuremath−t\ensuremath′\ensuremath−U model. It enhanced the long-range vertex contributions to the pairing correlations only for weak values of U.
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.
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To understand correlated insulating and unconventional superconducting states in twisted bilayer graphene, we perform a systematic study of spin and pairing correlations in an effective two-orbital Hubbard model, by using the ground-state constrained-path quantum Monte Carlo method. Our numerical simulations reveal that when only the on-site Hubbard UUU is considered, the long-range magnetic order develops for $U\ensuremath{\ge}3.2t$ at half filling. Upon doping away from half filling, an analysis based on the pairing correlations and corresponding vertex contributions identifies that pairing with the d+idd+idd+id symmetry is the dominant pairing channel. As the on-site Coulomb interaction is increased, both spin correlation and effective pairing interaction are enhanced simultaneously, indicating the intimate relation between magnetism and superconductivity. An inclusion of nearest neighbor Coulomb interaction VVV results in a suppression of the d+idd+idd+id superconductivity, but it can survive in the small VVV regime. Our findings are useful for clarifying the ongoing controversy on the superconducting pairing symmetry in twisted bilayer graphene.