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arXiv:cond-mat/0409141 · Physical Review B

U−J synergy effect for high- Tc superconductors

Liliana Arrachea, Dražen Zanchi

Published Feb 28, 2005• 12 citations
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Abstract

Using the renormalization group with included self-energy effects and exact diagonalization of small clusters we investigate the ground-state phase diagram of a two-dimensional extended Hubbard model with nearest-neighbor exchange interaction $J$, in addition to the local Coulomb repulsion $U$. The main instabilities are antiferromagnetism close to half filling and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the doped system. We find that self-energy effects are fatal for superconductivity in the repulsive Hubbard model (i.e., $J=0$, $U>0$). The superconductivity is triggered by finite $J$. The combined action of $J$ and $U$ interactions provide a remarkably efficient, mechanism to enhance both ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconducting and antiferromagnetic correlations.

DOI
10.1103/physrevb.71.064519

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Using the renormalization group with included self-energy effects and exact diagonalization of small clusters we investigate the ground-state phase diagram of a two-dimensional extended Hubbard model with nearest-neighbor exchange interaction JJJ, in addition to the local Coulomb repulsion UUU. The main instabilities are antiferromagnetism close to half filling and dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ superconductivity in the doped system. We find that self-energy effects are fatal for superconductivity in the repulsive Hubbard model (i.e., J=0J=0J=0, U>0U>0U>0). The superconductivity is triggered by finite JJJ. The combined action of JJJ and UUU interactions provide a remarkably efficient, mechanism to enhance both dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ superconducting and antiferromagnetic correlations.
Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range ddd-wave pair field term, which precipitates a superconducting state in the ddd-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the ddd-wave pair/spin/charge-density matrices. The calculations show a ddd-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion UUU and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. We also demonstrate that negative ${t}^{\ensuremath{'}}$ plays an important role in facilitating ddd-wave superconductivity.
By using the field-theoretical techniques combining bosonization with renormalization group, we study a one-dimensional (1D) model of interacting electrons with on-site repulsion (U > 0), nearest-neighbor (nn) exchange (J) and correlated-hopping (t2, t3) interactions at weak coupling. In the case of a half-filled band, the two-body interaction t2 does not influence phase diagram of the model, while the presence of three-body interaction t3 makes the physics of the system highly non-trivial. By a Hartree–Fock decoupling, the effects of t3 bring about hopping of pairs, V-like (nn Coulomb interaction) and isotropic exchange terms in the reduced model Hamiltonian. Interestingly, a negative t3 provides a possibility for the occurrence of the triplet superconductivity in 1D system with purely repulsive interactions (U, J > 0). The ground state phase diagram including the insulating and superconducting phases is discussed analytically.
The coexistence or exclusivity of dx2−y2d_{x^{2} - y^{2}}dx2−y2​-wave superconducting (d-SC) and antiferromagnetic (AF) orders and instability toward phase separation (PS) are reconsidered for the square-lattice t–J model with the diagonal transfer (t′) term near half filling. To reliably treat the strong correlation including the local constraint of no double occupancy, we use a variational Monte Carlo method, in which the band-renormalization effect (BRE) is also incorporated. The results are compared with those recently obtained for the corresponding Hubbard model [J. Phys. Soc. Jpn. 85, 074701 (2016)]. It is found that BRE has a very strong effect on the AF order and greatly modifies the ground-state phase diagram in the t′–δ space (δ: doping rate) proposed in previous studies, especially for large |t′/t|. In a wide range of t′/t (|t′/t| ≤ 0.5) and for any underdoped δ (≲ \lesssim ≲ 0.15), the AF order arises for J/t = 0.3, similarly to in the Hubbard model. In contrast with the Hubbard model, however, the d-SC order also arises down to small δ in a wide range of t′/t (≳ \gtrsim ≳ −0.2) and coexists with the AF order even for t′/t < 0 (type-II AF regime). Furthermore, there is no instability toward PS for any t′/t and δ for J/t = 0.3.
The renormalization of the electron-phonon interaction by strong electronic correlations is studied using a one-band Hubbard model with infinite repulsion and nearest (t model) and nearest and second-nearest (tt\ensuremath{'} model) neighbor hopping terms and an on-site electron-phonon coupling. Using Hubbard's X operators and an extension from 2 to N degrees of freedom for the electrons the leading contributions for the electron self-energy and the vertex function in 1/N and the electron-phonon coupling constant are given and numerically evaluated for a square lattice. We find that the momentum dependence of the vertex function depends strongly on doping: For large dopings it is rather weak, with decreasing doping it becomes more and more pronounced leading to a strong reduction of the vertex at larger momentum transfers until, for very small dopings, the vertex essentially consists of a forward scattering peak with a width proportional to the doping. This behavior occurs both in the t and the tt\ensuremath{'} models and also in one dimension where analytic expressions are derived. Correlation effects also change ${\mathrm{\ensuremath{\alpha}}}^{2}$F in general: The full-symmetric component ${\mathrm{\ensuremath{\alpha}}}^{2}$F1{\mathit{F}}_{1}F1​ is in the t model somewhat, in the tt\ensuremath{'} model rather strongly suppressed, especially near half-filling; the other symmetry components ${\mathrm{\ensuremath{\alpha}}}^{2}$Fi{\mathit{F}}_{\mathit{i}}Fi​ with i=2,...,5 increase strongly with decreasing doping and are of similar magnitude as ${\mathrm{\ensuremath{\alpha}}}^{2}$F1{\mathit{F}}_{1}F1​ near half-filling.Including also direct Coulomb repulsion nontrivial symmetries such as d wave become more stable than the s-wave order parameter below a critical value for the doping even for the considered phonon-mediated superconductivity. Most dramatic, however, is the quenching of the resistivity due to electron-phonon scattering both in the t and the tt\ensuremath{'} models at intermediate and small dopings. This result may explain the absence of phonon features in the experimental transport coefficients of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ compounds. \textcopyright{} 1996 The American Physical Society.
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 4×44\times44×4 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 Hubbard model with local on-site repulsion is generally thought to possess a superconducting ground state for appropriate parameters, but the effects of more realistic long-range Coulomb interactions have not been studied extensively. We study the influence of these interactions on superconductivity by including nearest- and next-nearest-neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find that nearest and next-nearest neighbor interactions have thresholds above which they destabilize superconductivity regardless of whether they are attractive or repulsive, seemingly due to competing charge fluctuations.