The effect of a weak random potential on two-leg Hubbard ladders is investigated. The random potential is shown to induce Anderson localization except for attractive enough interactions, supressing completely d-wave superconductivity. These localization effects remain very strong even for many ladders coupled by Josephson coupling. Both dc and ac conductivities and localization lengths are obtained. Consequences for the superconducting ladder compound SrxCa14−xCu24O41+δ are discussed. The two-chain Hubbard ladder is a toy model of a metal with a spin-gap, reminiscent of the metallic phase of underdoped cuprates. Recent experiments[1] on the superconducting transition in Sr14−xCaxCu24O41 have been interpreted in the framework of this model. However, impurities are only considered as a source of holes and not a source of random potential although it is known that an infinitesimal disorder localizes all electronic states in one dimension. It is therefore important to investigate the disordered Hubbard ladder. The disordered Hubbard ladder is defined by the Hamiltonian: H = −t ‖ (c † i+1,p,σci,p,σ + c † i,p,σci+1,p,σ) − t⊥ i,p,σ i,σ
We investigate the ground-state properties of correlated three-leg ladders near 1/3 filling. We apply the density-matrix renormalization group method to the three-leg t-J ladder with strong interchain couplings and evaluate its pairing nature. When holes are doped into the spin-gapped state at 1/3 filling, we find that pair correlations develop with power-law decays while spin correlations decay exponentially. On the other hand, doping of electrons into the 1/3-filled state does not give rise to substantial pair correlations. We also discuss the hole-doped state in the three-leg Hubbard model to compare it with the pairing state in the t-J model. Our numerical demonstrations provide insights into the electronic properties of trilayer nickelate superconductors.
We revisit the ground state of the Hubbard model on two-legged ladders in this paper. We perform density matrix renormalization group (DMRG) calculations on large system sizes with large numbers of kept states and perform extrapolation of DMRG results with truncation errors in the converged region. We find that the superconducting correlation exponent
Ksc extracted from the pair-pair correlation is very sensitive to the position of the reference bond, reflecting a huge boundary effect on it. By systematically removing the effects from boundary conditions, finite sizes, and truncation errors in DMRG, we obtain more accurate values of
Ksc and ${K}_{\ensuremath{\rho}}$ with DMRG. With these exponents, we confirm that the two-legged Hubbard model is in the Luther-Emery liquid phase with ${K}_{sc}\ifmmode\cdot\else\textperiodcentered\fi{}{K}_{\ensuremath{\rho}}=1$ from tiny doping near half filling to
1/8 hole doping. When the doping is increased to $\ensuremath{\delta}⪆1/6$, the behaviors of charge, pairing, and spin correlations do not change qualitatively, but the relationship ${K}_{sc}\ifmmode\cdot\else\textperiodcentered\fi{}{K}_{\ensuremath{\rho}}=1$ is likely to be violated. With the further increase of the doping to $\ensuremath{\delta}=1/3$, the quasi-long-ranged charge correlation turns into a true long-ranged charge order, and the spin gap is closed, while the pair-pair correlation still decays algebraically. Our work provides a standard way to analyze the correlation functions when studying systems with open boundary conditions.