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arXiv:cond-mat/9705165 · Journal of the Physical Society of Japan

Superconducting, Ferromagnetic and Antiferromagnetic Phases in thet-t′Hubbard Model

Jose Vicente Alvarez, J. González, F. Guinea, María A. H. Vozmediano

Published Jun 15, 1998• 39 citations
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Abstract

We apply a renormalization group approach to the determination of the phase diagram of the t-t' Hubbard model at the Van Hove filling, as function of t'/t, for small values of U/t. The model presents ferromagnetic, antiferromagnetic and d-wave superconducting phases. Antiferromagnetism and d-wave superconductivity arise from the same interactions, and compete in the same region of parameter space.

DOI
10.1143/jpsj.67.1868

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We apply a renormalization group approach to the determination of the phase diagram of the t-t' Hubbard model at the Van Hove filling, as function of t'/t, for small values of U/t. The model presents ferromagnetic, antiferromagnetic and d-wave superconducting phases. Antiferromagnetism and d-wave superconductivity arise from the same interactions, and compete in the same region of parameter space.
Phase diagrams of the two-dimensional one-band $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model are obtained within the two-patch and temperature-cutoff many-patch renormalization group approaches. At small ${t}^{\ensuremath{'}}$ and at van Hove band fillings antiferromagnetism dominates, while with increasing ${t}^{\ensuremath{'}}$ or changing filling antiferromagnetism is replaced by d-wave superconductivity. Near ${t}^{\ensuremath{'}}=t/2$ and close to van Hove band fillings the system is unstable towards ferromagnetism. Away from van Hove band fillings this ferromagnetic instability is replaced by a region with dominating triplet p-wave superconducting correlations. The results of the renormalization-group approach are compared with the mean-field results and the results of the T-matrix approximation.
The $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model for the Fermi level near the van Hove singularity is considered within the renormalization group and parquet approaches. Interplay of ferromagnetic, antiferromagnetic, and superconducting channels is investigated, and the phase diagram of the model is constructed. In comparison with previous approaches, the account of ferromagnetic fluctuations suppresses superconducting pairing and, vice versa, the influence of the Cooper channel decreases the Curie temperature, so that the Stoner criterion is inapplicable even qualitatively.
The phase diagram of the two-dimensional extended one-band $U\ensuremath{-}V\ensuremath{-}J$ Hubbard model is considered within a mean-field approximation and two- and many-patch renormalization-group (RG) approaches near the Van Hove band fillings. At small ${t}^{\ensuremath{'}}$ and J>0,J>0,J>0, mean-field and many-patch RG approaches give similar results for the leading spin-density-wave (SDW) instability, while the two-patch RG approach that predicts a wide region of charge-flux (CF) phase becomes unreliable due to nesting effect. There is a complex competition between SDW, CF phases, and d-wave superconductivity at small ${t}^{\ensuremath{'}}$ in two- and many-patch RG approaches. The spin-flux phase, which is not stable at the mean-field level, is identified as a possible ground state at J<0J<0J<0 in both RG approaches. With increasing ${t}^{\ensuremath{'}}$ the results of all three approaches merge: d-wave superconductivity at J>0J>0J>0 and ferromagnetism at J<0J<0J<0 become the leading instabilities. For large enough V, the charge-density-wave state occurs.
We analyze the competition between antiferromagnetism and superconductivity in the two-dimensional Hubbard model by combining a functional renormalization group flow with a mean-field theory for spontaneous symmetry breaking. Effective interactions are computed by integrating out states above a scale ${\ensuremath{\Lambda}}_{\mathrm{MF}}$ in one-loop approximation, which captures in particular the generation of an attraction in the ddd-wave Cooper channel from fluctuations in the particle-hole channel. These effective interactions are then used as an input for a mean-field treatment of the remaining low-energy states, with antiferromagnetism, singlet superconductivity, and triplet $\ensuremath{\pi}$ pairing as the possible order parameters. Antiferromagnetism and superconductivity suppress each other, leaving only a small region in parameter space where both orders can coexist with a sizable order parameter for each. Triplet $\ensuremath{\pi}$ pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small.
Abstract Using the singular-mode functional renormalization group method, we studied the doping-dependent phase diagram of the two-dimensional extended Hubbard model on square lattice. At half-filling, a variety of states strongly compete, including spin-density wave, charge-density wave, phase separation, as well as d -wave and s -wave superconductivity (SC). Upon electron doping, the system exhibits a strong preference for superconducting states. At slight dopings, the spin-density wave phase is strongly suppressed, and d -wave SC region expands into positive U , V region. At moderate dopings, a region of degenerated p -wave superconductivities emerge for positive U and negative V . Our results demonstrate how doping tunes the dominant fluctuations, suppressing density waves and stabilizing unconventional superconducting states in two dimensions.