Two-chain Hubbard Model Research Articles

Weak-coupling phase diagram of the two-chain Hubbard model.

We present a general method for determining the phase diagram of systems of a finite number of one-dimensional Hubbard-like systems coupled by single-particle hopping with weak interactions. The technique is illustrated by detailed calculations for the two-chain Hubbard model, providing controlled results for arbitrary doping and interchain hopping. Of nine possible states which could occur in such a spin-1/2 ladder, we find seven at weak coupling. We discuss the conditions under which the model can be regarded as a one-dimensional analog of a superconductor. \textcopyright{} 1996 The American Physical Society.

Erratum: Superconducting phase of a two-chain Hubbard model

Erratum: Superconducting phase of a two-chain Hubbard model

Superconductivity in the Two-Chain Hubbard Model Including the Interchain Coulomb Interaction

Superconductivity in the Two-Chain Hubbard Model Including the Interchain Coulomb Interaction

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

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.

Superconducting phase of a two-chain Hubbard model.

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.

Insulating states of correlated electrons

The insulating states of three model systems, the two-chain Hubbard model, the two-layer two-dimensional Hubbard model, and the two-dimensional symmetric periodic Anderson model are discussed. All of these systems at half-filling have a charge gap but they can exhibit various types of spin gaps ranging from a vanishing spin gap in systems with strong antiferromagnetic correlations to a spin gap which is equal to the charge gap in the band-insulator regime. The interchain, interplane, or Anderson model f-d hybridization plays a key role in determining the spin-to-charge gap ratio and the nature of the insulating state.

Density matrix renormalization group calculations for doped Hubbard ladders

The properties of the two-chain Hubbard Model doped away from half-filling are investigated using the density matrix renormalization group. A finite spin gap exists over a range of interchain hopping strength t⊥. A resonating valence bond ansatz provides an intuitive picture of the origin of the spin liquid phase.

Superconductivity indications of the two-chain Hubbard model due to the two-band effect

Corroborating our assertion worked out in preceding papers that the two-chain Hubbard model has a superconducting (SC) parameter region, we report new results obtained by the Lanczos diagonalization method. The SC region indicated by SC pair correlation functions show the tendency to converge to a considerable definite region in the parameter space with increase of the system size. A certain SC correlation function reveals that the SC order parameters pertinent to the two bands have different signs. The SC pair operators at two rungs keep strong spatial correlation in our SC region in striking contrast to the non-SC region. Calculation of correlation exponent K ϱ allows us to get an SC parameter region which proves to be in a qualitative agreement with the above-mentioned one.

Reduced-density-matrix analysis of superconducting correlation in two-dimensional and two-chain Hubbard models.

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 2${\mathit{k}}_{\mathit{F}}$ charge correlation up to 32\ifmmode\times\else\texttimes\fi{}2 sites suggests that the 2${\mathit{k}}_{\mathit{F}}$ 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 ${\mathit{t}}_{\mathit{v}}$/t=1.4). We conclude the reduced-density-matrix analysis discussed here is needed to unveil the nature of Hubbard and related models.

Correlations in a two-chain Hubbard model.

Equal time spin--spin and pair field correlation functions are calculated for a two-chain Hubbard model using a density-matrix numerical renormalization group approach. At half-filling, the antiferromagnetic and pair field correlations both decay exponentially with the pair field having a much shorter correlation length. This is consistent with a gapped spin-liquid ground state. Below half--filling, the antiferromagnetic correlations become incommensurate and the spin gap persists. The pair field correlations appear to follow a power law decay which is similar to their non-interacting U=0 behavior.

Two-band mechanism of superconductivity in dimeric hubbard models

In the two-chain Hubbard model the on-site Coulomb repulsion generates a remarkably large pair-transfer coupling constant between bonding and antibonding orbitals of a dimer made of the two sites lying on the opposite chains and linked by a transfer energy. It leads to a pair-transfer interaction between two bands composed of these orbitals, promoting superconductivity (SC). Since it is found to be as large as intraband Coulomb coupling constants, our previous work suggests that SC can occur in this model. In fact we have obtained a clear indication of SC in restricted-size systems carrying out the exact-diagonalization with 6 electrons and a variational diagonalization with up to 14. The SC occurs in suitable band situations for a wide range of on-site Coulomb energies. We also obtained such an SC indication in a two-dimensional Hubbard model. We mention some candidate materials substantiating the present mechanism and suggest it to be quite general.

Superconducting transition of the two-chain Hubbard model indicated by diagonalization calculations

In the two-chain Hubbard system the on-site Coulumb interaction at each site generates a pair-transfer interaction between the two bands consisting of bonding and antibonding orbitals for the two sites located on the opposite chains and linked by the transverse transfer energy. It is shown to be as strong as the intraband repulsive interaction generated in the same way so that it can give rise to superconductivity due to the two-band effect. Verifying this reasoning, exact-and also variational-diagonalization calculations clearly indicate that a superconducting state arises in this system in an appropriate region of band and filling parameters for a wide range of Coulomb strengths. A scaling analysis with systems of electron number equal to 6, 10 and 14 supports the assertion that the superconductivity survives in the limit of infinite size. The essence of this mechanism looks relevant to a wide variety of systems including D[M(dmit) 2] 2 superconductors and high- T c oxides.