We investigate the influence of nonlocal interactions on superconducting correlations within the extended Hubbard model. In addition to the on-site Coulomb interaction and nearest-neighbor hopping, we include next-nearest-neighbor hopping together with several physically relevant nonlocal terms, namely nearest-neighbor Coulomb interaction, correlated hopping, exchange interaction, and pair hopping. Using Lanczos exact diagonalization on a $4\times4$ cluster, supported by projector quantum Monte Carlo simulations for selected parameter regimes, we analyze pairing correlations in both the s- and d-wave channels. We demonstrate that nonlocal interactions exert a highly nontrivial and symmetry-dependent influence on superconducting correlations. While the on-site repulsion in cooperation with next-nearest-neighbor hopping enhances d-wave pairing tendencies, correlated hopping and nearest-neighbor Coulomb interaction strongly promote s-wave correlations, whereas exchange and pair-hopping interactions can efficiently suppress superconductivity beyond relatively small critical strengths. When all nonlocal interactions are considered simultaneously, the resulting phase diagrams reveal a complex interplay and competition between different pairing symmetries. Our results highlight the crucial role of extended interactions in shaping the pairing landscape of strongly correlated systems and demonstrate that a comprehensive treatment beyond the minimal Hubbard model is essential for a realistic description of unconventional superconductivity.We investigate the influence of nonlocal interactions on superconducting correlations within the extended Hubbard model. In addition to the on-site Coulomb interaction and nearest-neighbor hopping, we include next-nearest-neighbor hopping together with several physically relevant nonlocal terms, namely nearest-neighbor Coulomb interaction, correlated hopping, exchange interaction, and pair hopping. Using Lanczos exact diagonalization on a $4\times4$ cluster, supported by projector quantum Monte Carlo simulations for selected parameter regimes, we analyze pairing correlations in both the s- and d-wave channels. We demonstrate that nonlocal interactions exert a highly nontrivial and symmetry-dependent influence on superconducting correlations. While the on-site repulsion in cooperation with next-nearest-neighbor hopping enhances d-wave pairing tendencies, correlated hopping and nearest-neighbor Coulomb interaction strongly promote s-wave correlations, whereas exchange and pair-hopping interactions can efficiently suppress superconductivity beyond relatively small critical strengths. When all nonlocal interactions are considered simultaneously, the resulting phase diagrams reveal a complex interplay and competition between different pairing symmetries. Our results highlight the crucial role of extended interactions in shaping the pairing landscape of strongly correlated systems and demonstrate that a comprehensive treatment beyond the minimal Hubbard model is essential for a realistic description of unconventional superconductivity.

arXiv:2606.20260Jun 18, 20260 citations

Correlation effects in the extended Hubbard model

Ryszard Taranko, E. Taranko

Physica B Condensed MatterOct 1, 19884 citations

The Extended Hubbard Model at Large Interaction

P. G. J. van Dongen

NATO ASI series. Series B : PhysicsJan 1, 19951 citation

Effects of nonlocal interactions on s- and d-wave superconducting correlations in the extended Hubbard model

Pavol Farkašovský

Abstract We investigate the influence of nonlocal interactions on superconducting correlations within the extended Hubbard model. In addition to the on-site Coulomb interaction and nearest-neighbor hopping, we include next-nearest-neighbor hopping together with several physically relevant nonlocal terms, namely nearest-neighbor Coulomb interaction, correlated hopping, exchange interaction, and pair hopping. Using Lanczos exact diagonalization on a $4\times 4$ 4 × 4 cluster, supported by projector quantum Monte Carlo simulations for selected parameter regimes, we analyze pairing correlations in both the s - and d -wave channels. We demonstrate that nonlocal interactions exert a highly nontrivial and symmetry-dependent influence on superconducting correlations. While the on-site repulsion in cooperation with next-nearest-neighbor hopping enhances d -wave pairing tendencies, correlated hopping and nearest-neighbor Coulomb interaction strongly promote s -wave correlations, whereas exchange and pair-hopping interactions can efficiently suppress superconductivity beyond relatively small critical strengths. When all nonlocal interactions are considered simultaneously, the resulting phase diagrams reveal a complex interplay and competition between different pairing symmetries. Our results highlight the crucial role of extended interactions in shaping the pairing landscape of strongly correlated systems and demonstrate that a comprehensive treatment beyond the minimal Hubbard model is essential for a realistic description of unconventional superconductivity.Abstract We investigate the influence of nonlocal interactions on superconducting correlations within the extended Hubbard model. In addition to the on-site Coulomb interaction and nearest-neighbor hopping, we include next-nearest-neighbor hopping together with several physically relevant nonlocal terms, namely nearest-neighbor Coulomb interaction, correlated hopping, exchange interaction, and pair hopping. Using Lanczos exact diagonalization on a $$4\times 4$$ 4 × 4 cluster, supported by projector quantum Monte Carlo simulations for selected parameter regimes, we analyze pairing correlations in both the s - and d -wave channels. We demonstrate that nonlocal interactions exert a highly nontrivial and symmetry-dependent influence on superconducting correlations. While the on-site repulsion in cooperation with next-nearest-neighbor hopping enhances d -wave pairing tendencies, correlated hopping and nearest-neighbor Coulomb interaction strongly promote s -wave correlations, whereas exchange and pair-hopping interactions can efficiently suppress superconductivity beyond relatively small critical strengths. When all nonlocal interactions are considered simultaneously, the resulting phase diagrams reveal a complex interplay and competition between different pairing symmetries. Our results highlight the crucial role of extended interactions in shaping the pairing landscape of strongly correlated systems and demonstrate that a comprehensive treatment beyond the minimal Hubbard model is essential for a realistic description of unconventional superconductivity.

The European Physical Journal PlusAug 3, 20261 citation

Atomic screening and intersite Coulomb repulsion in strongly correlated systems

M.B.J. Meinders, Jeroen van den Brink, J. Lorenzana +1 more

We consider the influence of a nearest-neighbor Coulomb interaction in an extended Hubbard model and introduce an interaction term which simulates atomic polarizabilities. The inclusion of atomic polarizabilities in the model has the effect of screening the on-site Coulomb interaction for charged excitations, unlike a neighbor Coulomb interaction which reduces energies of neutral local excitations, leaving the conductivity gap unchanged. This is supported by an exact diagonalization study on small, mainly one-dimensional, extended Mott-Hubbard systems. For large V, the system undergoes a phase transition from a spin-density wave (SDW) to a charge-density wave (CDW). It is shown that the SDW/CDW phase transition cannot be described correctly when using effective parameters, but that screening effects have to be included explicitly. Also other phases, one of which is ferroelectric, appear when atomic polarizabilities are included in the model Hamiltonian. We study ${\mathrm{C}}_{60}$ in terms of the degenerate extended Hubbard model with screening effects.We consider the influence of a nearest-neighbor Coulomb interaction in an extended Hubbard model and introduce an interaction term which simulates atomic polarizabilities. The inclusion of atomic polarizabilities in the model has the effect of screening the on-site Coulomb interaction for charged excitations, unlike a neighbor Coulomb interaction which reduces energies of neutral local excitations, leaving the conductivity gap unchanged. This is supported by an exact diagonalization study on small, mainly one-dimensional, extended Mott-Hubbard systems. For large V, the system undergoes a phase transition from a spin-density wave (SDW) to a charge-density wave (CDW). It is shown that the SDW/CDW phase transition cannot be described correctly when using effective parameters, but that screening effects have to be included explicitly. Also other phases, one of which is ferroelectric, appear when atomic polarizabilities are included in the model Hamiltonian. We study ${\mathrm{C}}_{60}$ in terms of the degenerate extended Hubbard model with screening effects.

Physical review. B, Condensed matterJul 15, 199527 citations

4\times4

cluster, supported by projector quantum Monte Carlo simulations for selected parameter regimes, we analyze pairing correlations in both the s- and d-wave channels. We demonstrate that nonlocal interactions exert a highly nontrivial and symmetry-dependent influence on superconducting correlations. While the on-site repulsion in cooperation with next-nearest-neighbor hopping enhances d-wave pairing tendencies, correlated hopping and nearest-neighbor Coulomb interaction strongly promote s-wave correlations, whereas exchange and pair-hopping interactions can efficiently suppress superconductivity beyond relatively small critical strengths. When all nonlocal interactions are considered simultaneously, the resulting phase diagrams reveal a complex interplay and competition between different pairing symmetries. Our results highlight the crucial role of extended interactions in shaping the pairing landscape of strongly correlated systems and demonstrate that a comprehensive treatment beyond the minimal Hubbard model is essential for a realistic description of unconventional superconductivity.

4\times 4

4 × 4 cluster, supported by projector quantum Monte Carlo simulations for selected parameter regimes, we analyze pairing correlations in both the s - and d -wave channels. We demonstrate that nonlocal interactions exert a highly nontrivial and symmetry-dependent influence on superconducting correlations. While the on-site repulsion in cooperation with next-nearest-neighbor hopping enhances d -wave pairing tendencies, correlated hopping and nearest-neighbor Coulomb interaction strongly promote s -wave correlations, whereas exchange and pair-hopping interactions can efficiently suppress superconductivity beyond relatively small critical strengths. When all nonlocal interactions are considered simultaneously, the resulting phase diagrams reveal a complex interplay and competition between different pairing symmetries. Our results highlight the crucial role of extended interactions in shaping the pairing landscape of strongly correlated systems and demonstrate that a comprehensive treatment beyond the minimal Hubbard model is essential for a realistic description of unconventional superconductivity.

{\mathrm{C}}_{60}

in terms of the degenerate extended Hubbard model with screening effects.