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arXiv:cond-mat/0207582 · Physical review. B, Condensed matter

Current-current correlations in a CuO3 model system

Bhargavi Srinivasan, Marie-Bernadette Lepetit

Published Jul 12, 2002• 9 citations
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Abstract

We study a three-band extended Hubbard model on a ${\mathrm{CuO}}_{3}$ system by the density-matrix renormalization group method. Our system has geometry similar to that of a section of the ${\mathrm{CuO}}_{2}$ plane of the copper-oxide superconductors. We have studied the effects of nearest-neighbor repulsions on the current-current correlations of two model ${\mathrm{CuO}}_{3}$ systems. We have calculated several types of staggered current correlations as a function of various model parameters such as interaction strengths and filling. We show that repulsive interactions are clearly capable of increasing the magnitude of the current-current correlations in both models studied. The long-distance behavior of the current-current correlations is qualitatively influenced by V. We show that repulsive interactions are capable of enhancing correlations involving at least one copper-oxygen rung over distances comparable to the length of the system. In some cases, V decreases the exponent corresponding to the power-law decay, leading to a considerable slowing down of the long-distance decay of the current-current correlations, compared to that of the Hubbard model.

DOI
10.1103/physrevb.66.024421

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Physical review. B, Condensed matter•May 1, 1993•19 citations
We study a three-band extended Hubbard model on a CuO3{\mathrm{CuO}}_{3}CuO3​ system by the density-matrix renormalization group method. Our system has geometry similar to that of a section of the CuO2{\mathrm{CuO}}_{2}CuO2​ plane of the copper-oxide superconductors. We have studied the effects of nearest-neighbor repulsions on the current-current correlations of two model CuO3{\mathrm{CuO}}_{3}CuO3​ systems. We have calculated several types of staggered current correlations as a function of various model parameters such as interaction strengths and filling. We show that repulsive interactions are clearly capable of increasing the magnitude of the current-current correlations in both models studied. The long-distance behavior of the current-current correlations is qualitatively influenced by V. We show that repulsive interactions are capable of enhancing correlations involving at least one copper-oxygen rung over distances comparable to the length of the system. In some cases, V decreases the exponent corresponding to the power-law decay, leading to a considerable slowing down of the long-distance decay of the current-current correlations, compared to that of the Hubbard model.
We study a 3-band extended Hubbard model on a CuO_3 system by the density matrix renormalization group (DMRG) method. Our system has geometry similar to that of a section of the CuO_2 plane of the copper-oxide superconductors. We have studied the effects of nearest-neighbour repulsions on the current-current correlations of two model CuO_3 systems. We show that repulsive interactions are clearly capable of increasing the magnitude of the current-current correlations in both models studied. The long-distance behavior of the current-current correlations is qualitatively influenced by V. We show that repulsive interactions are capable of enhancing correlations involving at least one copper-oxygen rung over distances comparable to the length of the system. In some cases, V decreases the exponent corresponding to the power-law decay, leading to a considerable slowing down of the long-distance decay of the current-current correlations, compared to that of the Hubbard model.
We study current-current correlations in the three-band Hubbard model for two-leg CuO ladders using the density-matrix renormalization group method. We find that these correlations decrease exponentially with distance for low doping but as a power law for higher doping. Their pattern is compatible with the circulating current (CC) phase which Varma has proposed to explain the pseudogaped metallic phase in underdoped high-temperature superconductors. However, for model parameters leading to a realistic ground state in the undoped ladder, the current fluctuations decay faster than the ddd-wavelike pairing correlations in the hole-doped state, at least up to a doping of 10%. Thus we conclude that no phase with CC order or dominant CC fluctuations occur in the three-band model of two-leg CuO ladders at low doping.
Using a strong-coupling approach, we show that staggered current vorticity does not obtain in the repulsive two-dimensional Hubbard model for large on-site Coulomb interactions, as in the case of the copper oxide superconductors. This trend also persists even when nearest-neighbor repulsions are present. However, staggered flux ordering emerges when attractive nearest-neighbor Coulomb interactions are included. Such ordering opens a gap along the $(\ensuremath{\pi},0)\ensuremath{-}(0,\ensuremath{\pi})$ direction and persists over a reasonable range of doping.
We study current-current correlations in the three-band Hubbard model for two-leg CuO ladders using the density-matrix renormalization group method. We find that these correlations decrease exponentially with distance for low doping but as a power law for higher doping. Their pattern is compatible with the circulating current (CC) phase which Varma has proposed to explain the pseudo-gaped metallic phase in underdoped high-temperature superconductors. However, for model parameters leading to a realistic ground state in the undoped ladder, the current fluctuations decay faster than the d-wave-like pairing correlations in the doped state. Thus we conclude that no phase with CC order or dominant CC fluctuations occur in the three-band model of two-leg CuO ladders.
A recent experiment has unveiled an anomalously strong electron-electron attraction in the one-dimensional copper-oxide chain ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$. While the effect of the near-neighbor electron attraction VVV in the one-dimensional extended Hubbard chain has been examined recently, its effect in the Hubbard model beyond the one-dimensional chain remains unclear. Here, we report a density matrix renormalization group study of the extended Hubbard model on long four-leg cylinders on the square lattice. We find that the near-neighbor electron attraction VVV can notably enhance the long-distance superconducting correlations while simultaneously suppressing the charge-density-wave (CDW) correlations. Specifically, for a modestly strong electron attraction, the superconducting correlations become dominant over the CDW correlations with a Luttinger exponent ${K}_{sc}\ensuremath{\sim}1$ and strong divergent superconducting susceptibility. Our results provide a promising way to realize long-range superconductivity in the doped Hubbard model. The relevance of our numerical results to cuprate materials is also discussed.
The ``fluctuation-exchange'' approximation, a Baym-Kadanoff theory used previously to treat the one-band Hubbard model, is used to investigate a three-band model for the CuO2{\mathrm{CuO}}_{2}CuO2​ planes in the cuprate superconductors. Attention is restricted to (a) nearest-neighbor copper-oxygen hopping and (b) a Hubbard-like Coulomb interaction on copper sites only. Orbital-occupancy factors are shown to be in good agreement with previous quantum simulation studies. An instability eigenvalue analysis confirms that, as in the one-band model, the most likely channel for superconductivity is a dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 singlet. The scale for onset of exponentially long-ranged antiferromagnetic correlations is compared with results for the one-band model, and the role of hybridization in reducing the effective Coulomb interaction is studied using a transformation to Wannier states.