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arXiv:cond-mat/9603076 · Physical review. B, Condensed matter

Phase separation and the existence of superconductivity in a one-dimensional copper-oxygen model

Anders W. Sandvik, Asle Sudbø

Published Aug 1, 1996• 11 citations
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Abstract

The phase-separation instability occurring with increasing nearest-neighbor repulsion $V$ in a two-band Hubbard model (CuO chain) is discussed. Quantum Monte Carlo simulations indicate that this transition is strongly discontinuous if the filling fraction $〈n〉$ is close to 1 (half-filled lower band). Spin-density-wave fluctuations then dominate before phase separation. Superconducting fluctuations dominate in the neighborhood of phase separation only at considerably higher doping levels, where the transition to the phase-separated state is much smoother.

DOI
10.1103/physrevb.54.r3746

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The phase-separation instability occurring with increasing nearest-neighbor repulsion VVV in a two-band Hubbard model (CuO chain) is discussed. Quantum Monte Carlo simulations indicate that this transition is strongly discontinuous if the filling fraction 〈n〉〈n〉〈n〉 is close to 1 (half-filled lower band). Spin-density-wave fluctuations then dominate before phase separation. Superconducting fluctuations dominate in the neighborhood of phase separation only at considerably higher doping levels, where the transition to the phase-separated state is much smoother.
A two-band Hubbard model describing a CuO chain is studied using quantum Monte Carlo simulation. The Luttinger-liquid exponent K ρ is extracted as a function of the nearest-neighbor repulsion V , at hole fillings ⟨ n ⟩ between 1 (half-filled lower band) and 2. Evidence is presented for the existence of a regime with dominant singlet superconducting fluctuations and a gap in the spin excitation spectrum at ⟨ n ⟩ = 1.75, in the neighborhood of the V for which the system phase separates. Closer to half-filling (⟨ n ⟩≲1.6), spin-density-wave fluctuations always dominate.
We study the phase diagram of a one-dimensional Hubbard model where, in addition to the standard nearest-neighbor hopping t, we also include a next-to-nearest-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$. For strong enough on-site repulsion, this model has a transition at half filling from a magnetic insulator with gapless spin excitations at small ${\mathit{t}}^{\ensuremath{'}}$/t to a dimerized insulator with a spin gap at larger ${\mathit{t}}^{\ensuremath{'}}$/t. We show that upon doping this model exhibits quite interesting features, which include the presence of a metallic phase with a spin gap and dominant superconducting fluctuations, in spite of the repulsive interaction. More interestingly, we find that this superconducting phase can be reached upon hole doping the magnetic insulator. The connections between this model and the two chain models, recently object of intensive investigations, are also discussed. \textcopyright{} 1996 The American Physical Society.
A one-dimensional two-band Hubbard model describing CuO chains is considered in the limit of zero bandwidth. Onsite and nearest-neighbor Coulomb interactions are included in the description. Various density correlation functions are calculated exactly at arbitrary concentration of holes. For increasing values of the intersite Coulomb interaction V, the system is driven towards both a charge-transfer instability and a phase separation instability when doped away from half filling. In the case of one hole added to the half-filled system, it is shown that a hole binds to a biexciton. Three-body bound states recently proposed to produce the marginal Fermi-liquid spectrum also occur naturally in the model, but a finite amount of doping away from half filling is necessary for them to form to an appreciable extent in the thermodynamic limit.
We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on-site interaction U and a nearest-neighbor interaction V. We focus on the ground state phases of the model in the $V\ensuremath{\gg}U$ region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=VPS.{V=V}_{\mathrm{PS}}.V=VPS​. Using quantum Monte Carlo methods on lattices much larger than in previous Lancz\"os diagonalization studies, we determine the boundary of phase separation, the Luttinger-liquid correlation exponent ${K}_{\ensuremath{\rho}},$ and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state reenters from phase separation as the electron density is increased towards half filling. For V<VPS,V<{V}_{\mathrm{PS}},V<VPS​, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger liquid with ${K}_{\ensuremath{\rho}}<1,$ but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger liquid.
Cooperation and competition between the antiferromagnetic, ddd-wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength UUU below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.
The variational Monte Carlo method is used to study possible superconducting states of a two-dimensional extended Hubbard model on a copper-oxygen lattice. It is found that d-wave and extended s-wave superconducting variational wave functions can have lower energy than the corresponding normal state for different parameter regions, while simple s-wave superconductivity is never favored. Increasing the nearest-neighbor repulsion and decreasing the copper-oxygen level separation can promote extended s-wave superconductivity and inhibit d-wave superconductivity.