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arXiv:cond-mat/9403059 · Physical Review Letters

Asymptotically exact solution of a local copper-oxide model

Guang-Ming Zhang, Lu Yu

Published Apr 11, 1994• 13 citations
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Abstract

We present an asymptotically exact solution of a local copper-oxide model abstracted from the multiband models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling regime, we find an exactly solved line, which crosses the quantum critical point of the mixed valence regime separating two different Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is formed near the chemical potential, and a marginal-FL spectrum can be derived for the spin and charge susceptibilities.

DOI
10.1103/physrevlett.72.2474

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•Jan 1, 1994•3 citations
We present an asymptotically exact solution of a local copper-oxide model abstracted from the multiband models. The phase diagram is obtained through the renormalization-group analysis of the partition function. In the strong coupling regime, we find an exactly solved line, which crosses the quantum critical point of the mixed valence regime separating two different Fermi-liquid (FL) phases. At this critical point, a many-particle resonance is formed near the chemical potential, and a marginal-FL spectrum can be derived for the spin and charge susceptibilities.
We solve for the properties of an impurity model abstracted from a model of copper oxide superconductors. At mixed valence, provided that Friedel's screening condition is satisfied, the marginal-Fermi-liquid spectrum is obtained for the spin and charge susceptibilities. The frequency dependence of the self-energies is \ensuremath{\Sigma}(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\omega} ln\ensuremath{\omega}+i\ensuremath{\omega}. This critical point is surrounded by two different Fermi-liquid phases. A simplified two-impurity version of this model is also addressed, and presents similar features, including a logarithmic divergence for coherent pair susceptibility.
The t-J model has been proposed to describe the physics of copper oxide planes in high-temperature superconductors. A real-space quantum renormalization-group method is developed in order to study the t-J Hamiltonian in a square lattice. The zero-temperature phase diagram is analysed for electron concentrations near the half-filled band and ratio J/t. A critical line is found that separates two distinct regions: one of a gas of holes in an antiferromagnetic background, and the other consisting of a phase in which holes segregate into a hole-rich and a pure antiferromagnetic region, as demonstrated by chemical-potential eigenvalue calculations near the phase attractor. The results are close to the experimental observations.
The phase diagram of the copper-oxide chain as a function of density and the nearest-neighbour Coulomb interaction, V, is determined. Phase separation takes place above a critical value of VVV when the Cu2+ to Cu+ valence fluctuations dominate. In the proximity of the phase separation boundary the superconducting correlations are the most divergent. We identify the parameter regions where the Luttinger Liquid theory applies and calculate the contours of the charge-charge correlation exponent K_ρ. We show that anomalous flux quantization occurs as K_ρ diverges. At n = 1, for V > t, a gap opens in the spectrum and the ground state is a charge-density wave.
The phase diagram of the copper-oxide chain as a function of density and the nearest-neighbour Coulomb interaction, V , is determined. Phase separation takes place above a critical value of V when the Cu 2+ → Cu + valence fluctuations dominate. In the proximity of the phase separation boundary the superconducting correlations are the most divergent. We identify the parameter regions where the Luttinger-liquid theory applies and calculate the contours of the charge-charge correlation exponent K ρ . We show that anomalous flux quantization occurs as K ρ diverges. At n = 1, for V > t , a gap opens in the spectrum and the ground state is a charge density wave.
The phase diagram of the copper-oxide chain as a function of density and the nearest-neighbour Coulomb interaction, V, is determined. Phase separation takes place above a critical value of V when the Cu 2+ → Cu + valence fluctuations dominate. In the proximity of the phase separation boundary the superconducting correlations are the most divergent. We identify the parameter regions where the Luttinger Liquid theory applies and calculate the contours of the charge-charge correlation exponent Kρ. We show that anomalous flux quantization occurs as Kρ diverges. At n = 1, for V> t, a gap opens in the spectrum and the ground state is a charge-density wave.