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1 Induced Order in Nonequivalent Two-Leg Hubbard Ladder

Hiroyuki Yoshizumi, Takami Tohyama, Takao Morinari

Published Nov 20, 2012• 2 citations
OpenAlex

Abstract

Motivated by the presence of different orders in multilayered high-temperature superconductors, we examine a model consisting of nonequivalent two Hubbard chains coupled by interchain hopping by using the density-matrix renormalization group (DMRG) and a mean-field theory. As an example, we consider a system with noninteracting chain without order and a Hubbard chain with strong antiferromagnetic (AF) spin-density-wave correlation. We find that the magnitude of the interchain hopping controls the strength of induced AF correlation as well as that of original one. It is also found that the induced AF correlation decreases with increasing the magnitude of the original correlation. Implications to the multilayered system are discussed. Recently the coexistence of antiferromagnetism and superconductivity has been reported in multilayered high-Tc cuprate superconductors from nuclear magnetic resonance experiments. 1),2) In the superconductors, there are different layers whose carrier concentrations are unequal. When the concentration is small (large), antiferromagnetic

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Induced Order in Nonequivalent Two-Leg Hubbard Ladder

H. Yoshizumi, T. Tohyama, T. Morinari

Motivated by the presence of different orders in multilayered high-temperature superconductors, we examine a model consisting of nonequivalent two Hubbard chains coupled by interchain hopping by using the density-matrix renormalization group (DMRG) and a mean-field theory. As an example, we consider a system with noninteracting chain without order and a Hubbard chain with strong antiferromagnetic (AF) spin-density-wave correlation. We find that the magnitude of the interchain hopping controls the strength of induced AF correlation as well as that of original one. It is also found that the induced AF correlation decreases with increasing the magnitude of the original correlation. Implications to the multilayered system are discussed.

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Motivated by the presence of different orders in multilayered high-temperature superconductors, we examine a model consisting of nonequivalent two Hubbard chains coupled by interchain hopping by using the density-matrix renormalization group (DMRG) and a mean-field theory. As an example, we consider a system with noninteracting chain without order and a Hubbard chain with strong antiferromagnetic (AF) spin-density-wave correlation. We find that the magnitude of the interchain hopping controls the strength of induced AF correlation as well as that of original one. It is also found that the induced AF correlation decreases with increasing the magnitude of the original correlation. Implications to the multilayered system are discussed. Recently the coexistence of antiferromagnetism and superconductivity has been reported in multilayered high-Tc cuprate superconductors from nuclear magnetic resonance experiments. 1),2) In the superconductors, there are different layers whose carrier concentrations are unequal. When the concentration is small (large), antiferromagnetic
Motivated by the presence of different orders in multilayered high-temperature superconductors, we examine a model consisting of nonequivalent two Hubbard chains coupled by interchain hopping by using the density-matrix renormalization group (DMRG) and a mean-field theory. As an example, we consider a system with noninteracting chain without order and a Hubbard chain with strong antiferromagnetic (AF) spin-density-wave correlation. We find that the magnitude of the interchain hopping controls the strength of induced AF correlation as well as that of original one. It is also found that the induced AF correlation decreases with increasing the magnitude of the original correlation. Implications to the multilayered system are discussed.
The effect of antiferromagnetic interchain coupling in alternating spin-(1,1/2) chains is studied by means of spin-wave theory and density-matrix renormalization group (DMRG). In particular, two limiting cases are investigated, the two-leg ladder and its two-dimensional (2D) generalization. Results of the ground-state properties like energy, spin gap, magnetizations, and correlation functions are reported for the whole range of the interchain coupling ${J}_{\ensuremath{\perp}}.$ For the 2D case the spin-wave results predict a smooth dimensional crossover from 1D to 2D keeping the ground state always ordered. For the ladder system, the DMRG results show that any ${J}_{\ensuremath{\perp}}>0$ drives the system to a gapped ground state. Furthermore the behavior of the correlation functions closely resemble the uniform spin-1/2 ladder. For ${J}_{\ensuremath{\perp}}$ lower than 0.3, however, the gap behaves quadratically as $\ensuremath{\Delta}\ensuremath{\sim}{0.6J}_{\ensuremath{\perp}}^{2}.$ Finally, it is argued that the behavior of the spin gap for an arbitrary number of mixed coupled spin chains is analogous to that of the uniform spin-1/2 chains.
The one-band t–J model captures strong correlations in cuprate high-temperature superconductors. It accounts for the various intertwined spin and charge orders, and the superconductivity in the phase diagrams. To see the correlation effect on the intertwined orders, we implement the density matrix renormalization group method to simulate the t–J model in a small J case with t/J = 10, which is in a deeper Mott region than that with t/J ≃ 3 in cuprate superconducting compounds. We examine the results on a six-leg lattice with both the nearest and next-nearest-neighbor hoppings and antiferromagnetic coupling, and find the absence of superconductivity and enhanced intertwined spin and charge orders in the phase diagram. Besides the stripe phases, we find a new SDW + CDW phase in which the spin modulation is a (π, π) antiferromagnetism, while the wavelength of the charge modulation is shorter than that of the stripe phases. Our results suggest the enhanced intertwined orders and suppressed superconductivity in the deep Mott region.
We calculate the phase diagram of a ladder system, with a Hubbard interaction and an interchain coupling ${t}_{\ensuremath{\perp}}$. We use a renormalization-group method, in a one loop expansion, introducing an original method to include ${k}_{\ensuremath{\Vert}}$ dependence of couplings. We also classify the order parameters corresponding to ladder instabilities. We obtain different results, depending on whether we include ${k}_{\ensuremath{\Vert}}$ dependence or not. When we do so, we observe a region with large antiferromagnetic fluctuations, in the vicinity of small ${t}_{\ensuremath{\perp}}$, followed by a superconducting region with a simultaneous divergence of the spin density waves channel. We also investigate the effect of a nonlocal backward interchain scattering: we observe, on one hand, the suppression of singlet superconductivity and of spin density waves, and, on the other hand, the increase of charge density waves and, for some values of ${t}_{\ensuremath{\perp}}$, of triplet superconductivity. Our results eventually show that ${k}_{\ensuremath{\Vert}}$ is an influential variable in the renormalization-group flow, for this kind of system.
We propose a doped two-leg spin-1/21/21/2 diagonal ladder model (or a composite spin model) to simulate a doped spin-1 chain. By using the density matrix renormalization group method for an open chain, we find that the ground state hosts a dominant singlet dxy{d}_{xy}dxy​-wave superconducting correlation with features similar to those of the spin-1 Haldane phase. Meanwhile, we apply the renormalized mean-field theory to the model and obtain a dxy{d}_{xy}dxy​-wave superconducting state. The superconducting order exhibits a domelike shape as a function of hole concentration $\ensuremath{\delta}$. Our work provides a physical understanding of the origin of dxy{d}_{xy}dxy​ pairing symmetry, which originates from antiferromagnetic Heisenberg interaction in the diagonal direction, and the intrachain hopping term makes it stable.
Correlated-electron theories of superconductivity in layered cuprates often start from the premise of a gapped spin-liquid phase proximate to the superconducting state. This assumption is justified based on analytical and numerical demonstrations of a superconducting Luther-Emery phase in the doped 2-leg one-band Hubbard ladder, and the perceived analogy between coupled ladders and the two-dimensional CuO2{\mathrm{CuO}}_{2}CuO2​ layer. We demonstrate from accurate density matrix renormalization group studies the absence of the superconducting Luther-Emery phase in the doped 2-leg three-band ladder consisting of both copper and oxygen, even as the spin gap is large in the undoped three-band ladder. For realistic oxygen-oxygen hopping and Hubbard repulsion on the oxygen atoms, density-density rather than pairing correlations are dominant at long range. This result is equally valid whether or not the oxygens outside the ladder proper, over and above the rung and leg oxygens, are included in the computation. These results demonstrate the critical importance of oxygen orbitals, and raise disturbing questions about the applicability of many of the existing correlated-electron theories of superconductivity.