Phase Separation and Superconductivity in the Copper Oxide Chain.

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 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.

arXiv:cond-mat/9407067Europhysics Letters (EPL)Dec 20, 19943 citations

Large Phase Separation and Superconductivity in the Copper Oxide Chain

C. Vermeulen, W. Barford, Eduardo R. Gagliano

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 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 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.

arXiv:cond-mat/9407064Jul 13, 19940 citations

Possible exotic phases in the one-dimensional extended Hubbard model

Rudolf Torsten Clay, Anders W. Sandvik, David K Campbell

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 ${V=V}_{\mathrm{PS}}.$ 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 $V<{V}_{\mathrm{PS}},$ 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.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 ${V=V}_{\mathrm{PS}}.$ 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 $V<{V}_{\mathrm{PS}},$ 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.

arXiv:cond-mat/9810010Physical review. B, Condensed matterFeb 15, 199965 citations

Pairing fluctuations in a one-dimensional copper oxide model

Ellen B. Stechel, Asle Sudbø, Thierry Giamarchi +1 more

The exact ground-state energy ${\mathit{E}}_{0}$ (\ensuremath{\Phi}) is calculated for a one-dimensional copper-oxide model defined on a ring of finite length L, threaded by an external flux \ensuremath{\Phi}. It includes on-site and nearest-neighbor intersite Coulomb repulsion V, as well as a nonzero bare ``oxide'' gap ${\mathrm{\ensuremath{\Delta}}}_{0}$ between the orbitals in the unit cell. The correlation exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ of the corresponding low-energy Hamiltonian shows that singlet (extended s-wave) superconductivity has the most rapidly diverging susceptibility as T\ensuremath{\rightarrow}0 (${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1). This superconducting phase is located close to a phase-separation instability of the model, indicated by ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\rightarrow}\ensuremath{\infty}. Longer range of the Coulomb interaction tends to frustrate phase separation, enhances the range of V for which ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1, and slightly broadens the regime of V where 1${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\infty}.The exact ground-state energy ${\mathit{E}}_{0}$(\ensuremath{\Phi}) is calculated for a one-dimensional copper-oxide model defined on a ring of finite length L, threaded by an external flux \ensuremath{\Phi}. It includes on-site and nearest-neighbor intersite Coulomb repulsion V, as well as a nonzero bare ``oxide'' gap ${\mathrm{\ensuremath{\Delta}}}_{0}$ between the orbitals in the unit cell. The correlation exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ of the corresponding low-energy Hamiltonian shows that singlet (extended s-wave) superconductivity has the most rapidly diverging susceptibility as T\ensuremath{\rightarrow}0 (${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1). This superconducting phase is located close to a phase-separation instability of the model, indicated by ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\rightarrow}\ensuremath{\infty}. Longer range of the Coulomb interaction tends to frustrate phase separation, enhances the range of V for which ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1, and slightly broadens the regime of V where 1${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\infty}.

Physical review. B, Condensed matterJan 1, 199517 citations

Superconductivity and spin gap in the high-doping regime of a CuO chain model

Anders W. Sandvik, Asle Sudbø

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.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.

Europhysics Letters (EPL)Nov 20, 19967 citations

Phase diagram of the one-dimensionalt-Jmodel

Masao Ogata, Marco U. Luchini, Sandro Sorella +1 more

The phase diagram of the one-dimensional t-J model is investigated by analyzing the results of exact diagonalization and the exact solutions at J/t=0 and 2. Phase separation takes place above a critical value of J around ${\mathit{J}}_{\mathit{c}}$ /t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.The phase diagram of the one-dimensional t-J model is investigated by analyzing the results of exact diagonalization and the exact solutions at J/t=0 and 2. Phase separation takes place above a critical value of J around ${\mathit{J}}_{\mathit{c}}$/t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.

Physical Review LettersMay 6, 1991317 citations

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 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.

{V=V}_{\mathrm{PS}}.

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<{V}_{\mathrm{PS}},

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.

The exact ground-state energy

{\mathit{E}}_{0}

(\ensuremath{\Phi}) is calculated for a one-dimensional copper-oxide model defined on a ring of finite length L, threaded by an external flux \ensuremath{\Phi}. It includes on-site and nearest-neighbor intersite Coulomb repulsion V, as well as a nonzero bare ``oxide'' gap ${\mathrm{\ensuremath{\Delta}}}_{0}$ between the orbitals in the unit cell. The correlation exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ of the corresponding low-energy Hamiltonian shows that singlet (extended s-wave) superconductivity has the most rapidly diverging susceptibility as T\ensuremath{\rightarrow}0 (${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1). This superconducting phase is located close to a phase-separation instability of the model, indicated by ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\rightarrow}\ensuremath{\infty}. Longer range of the Coulomb interaction tends to frustrate phase separation, enhances the range of V for which ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1, and slightly broadens the regime of V where 1${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\infty}.

{\mathit{J}}_{\mathit{c}}

/t=2.5--3.5 depending on the electron density. In the small-J region, Tomonaga-Luttinger liquid theory holds and its correlation exponents are calculated as a function of J/t and the electron density. Superconducting correlations become dominant in a region between the solvable case (J/t=2) and phase separation. A spin-gap region is also found at low density.