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arXiv:supr-con/9508003 · Physical review. B, Condensed matter

Superconducting, magnetic, and charge correlations in the doped two-chain Hubbard model

Yoshihiro Asai

Published Oct 1, 1995• 10 citations
arXivHTMLPDF

Abstract

We have studied the superconducting, magnetic, and charge correlation functions and the spin excitation spectrum in the doped two-chain Hubbard model by projector Monte Carlo and Lanczos diagonalization methods. The exponent of the interchain singlet superconducting correlation function, \ensuremath{\gamma}, is found to be close to 2.0 as long as two distinct noninteracting bands cross the Fermi level. Magnetic and charge correlation functions decay more rapidly than or as fast as the interchain singlet superconducting correlation function along the chains. The superconducting correlation in the doped two-chain Hubbard model is the most long-range correlation studied here. Implications of the results for the possible universality class of the doped two-chain Hubbard model are discussed.

DOI
10.1103/physrevb.52.10390

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We have studied the superconducting, magnetic, and charge correlation functions and the spin excitation spectrum in the doped two-chain Hubbard model by projector Monte Carlo and Lanczos diagonalization methods. The exponent of the interchain singlet superconducting correlation function, \ensuremath{\gamma}, is found to be close to 2.0 as long as two distinct noninteracting bands cross the Fermi level. Magnetic and charge correlation functions decay more rapidly than or as fast as the interchain singlet superconducting correlation function along the chains. The superconducting correlation in the doped two-chain Hubbard model is the most long-range correlation studied here. Implications of the results for the possible universality class of the doped two-chain Hubbard model are discussed.
We have calculated the largest eigenvalues of the reduced density matrix of the singlet superconducting correlation function and pair-field susceptibility in two-dimensional and two-chain Hubbard models with quantum Monte Carlo methods. A singlet superconducting channel opens upon doping but is otherwise closed at half-filling when U/t=4. The interaction vertex contribution to the largest eigenvalue of the singlet pair-field susceptibility grows with a power law as temperature is decreased. With these two observations, we revise our previous understanding of the interaction vertex in the two-dimensional Hubbard model. We observe that some phases reside in the two-chain Hubbard model. An analysis of the 2kF{\mathit{k}}_{\mathit{F}}kF​ charge correlation up to 32\ifmmode\times\else\texttimes\fi{}2 sites suggests that the 2kF{\mathit{k}}_{\mathit{F}}kF​ correlation is dominant over the superconducting correlation (0.25\ensuremath{\le}${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\le}1.00) in the two-component Luttinger-liquid phase (U/t=2 and tv{\mathit{t}}_{\mathit{v}}tv​/t=1.4). We conclude the reduced-density-matrix analysis discussed here is needed to unveil the nature of Hubbard and related models.
The exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ and pair-field-correlation functions are calculated for a two-chain Hubbard model with an exact numerical diagonalization method. Our calculations clearly indicate that a superconducting phase appears for a wide range of Coulomb strength, where ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ and pair-field correlation functions are enhanced compared to the noninteracting system. The interchain pairing appears predominantly and thus our mechanism predicts an anisotropic superconductivity.
Numerical results obtained from Monte Carlo simulation in the ground state and at finite temperatures as well as the exact diagonalization and the transfer matrix method are reported. Efficiency of the Monte Carlo method in the ground state is examined. Spin, charge and superconducting correlations are investigated for the Hubbard and the t - J model in one and two dimensions. The momentum distribution in the one-dimensional Hubbard model shows fermi-liquid-like behavior at least in two orders of magnitude smaller energy scale than the band width. The short-range incommensurate spin correlation is observed and analyzed in the doped Hubbard and the t - J model both in one and two dimensions. In the ground state, the superconducting correlation shows the absence of system size dependence in two dimensions at the filling smaller than 0.8 and in one dimension at any filling. The binding energy of two fermions and the spin and charge distortion around an itinerant fermion are also discussed in the t - J and the coupled spin-fermion model.
The properties of the two-chain Hubbard model doped away from half-filling are investigated with the density matrix renormalization group. The charge gap is found to vanish, but a finite spin gap phase exists over a range of interchain hopping strength t ⊥ . In this phase, there are modified d x 2 - y 2 pairing correlations which exhibit a power law decay while both the 2 k F spin and charge correlations are short range. Above a critical value of t ⊥ , the system behaves as a Luttinger liquid.
Magnetic and superconducting pairing correlation functions in a general class of Hubbard models, the t - J model and a single-band Hubbard model with additional bond - charge interaction are investigated. Some rigorous upper bounds of the corresponding correlation functions are obtained. It is found that the decay of the spin - spin correlation function with temperature in the general Hubbard models cannot be slower than the inverse square law at low temperatures and the inverse law at high temperatures, while the on-site pairing correlation function cannot be slower than the inverse law. An upper bound for the average energy of the t - J model is found. The upper bounds for the spin - spin and the electron pairing correlation functions in the t - J model as well as in the Hubbard model with bond - charge interaction are also obtained. These bounds are expected to provide certain standards for approximate methods. In some special cases, these bounds rule out the possibility of corresponding magnetic and pairing long-range order.
We investigate the two-chain Hubbard model including the next nearest-neighbor transfer energies both in the interchain and intrachain directions by use of the exact-diagonalization and the variational Monte Carlo methods. We find that superconducting correlation functions are enhanced in such a situation where the density of states of the antibonding band in the neighborhood of the Fermi level enlarges due to the above-mentioned transfer energies, especially, in the situation where the Fermi level is located a little above the bottom of the antibonding band. In such a situation we find from the calculated momentum distribution function that this system is in almost one-band situation close to the two-band one. The relevance to ladder-type superconductor Sr 14- x Ca x Cu 24 O 41 is asserted.