Physical review. B, Condensed matter

Bethe-Salpeter eigenvalues and amplitudes for the half-filled two-dimensional Hubbard model

Niyazi Bulut, Douglas J. Scalapino, Steven R. White

Published Jun 1, 1993• 50 citations

Abstract

Monte Carlo simulations are used to determine the eigenvalues and eigenfunctions of the particle-hole and particle-particle Bethe-Salpeter equations for 8\ifmmode\times\else\texttimes\fi{}8 half-filled Hubbard lattice with U/t=4 and U/t=8. In the particle-hole channel, the dominant eigenvalue corresponds to the Q=(\ensuremath{\pi},\ensuremath{\pi}) antiferromagnetic correlations. In the particle-particle channel the amplitude of the leading low-temperature eigenvalue is an even-frequency ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ singlet. Odd-frequency p-wave-singlet and s-wave-triplet amplitudes are also found.

DOI: 10.1103/physrevb.47.14599

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Physical review. B, Condensed matter

Bethe-Salpeter eigenvalues and amplitudes for the half-filled two-dimensional Hubbard model

Niyazi Bulut, Douglas J. Scalapino, Steven R. White

Published Jun 1, 1993• 50 citations

Publisher

Abstract

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

singlet. Odd-frequency p-wave-singlet and s-wave-triplet amplitudes are also found.

DOI: 10.1103/physrevb.47.14599

Related papers

Order-parameter symmetries for magnetic and superconducting instabilities: Bethe-Salpeter analysis of functional renormalization-group solutions

A. A. Katanin, A. P. Kampf

The Bethe-Salpeter equation is combined with the temperature-cutoff functional renormalization group approach to analyze the order parameter structure for the leading instabilities of the 2D $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model. We find significant deviations from the conventional $s$ -, $p$ -, or $d$ -wave forms, which is due to the frustration of antiferromagnetism at small and intermediate ${t}^{\ensuremath{'}}$. With adding a direct antiferromagnetic spin-exchange coupling the eigenfunctions in the particle-hole channel have extended $s$ -wave form, while in the particle-particle singlet pairing channel a higher angular momentum component arises besides the standard ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave component, which flattens the angular dependence of the gap. For ${t}^{\ensuremath{'}}$ closer to $t∕2$ we find a delicate competition of ferromagnetism and triplet pairing with a nontrivial pair-wavefunction.The Bethe-Salpeter equation is combined with the temperature-cutoff functional renormalization group approach to analyze the order parameter structure for the leading instabilities of the 2D $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}$ Hubbard model. We find significant deviations from the conventional $s$-, $p$-, or $d$-wave forms, which is due to the frustration of antiferromagnetism at small and intermediate ${t}^{\ensuremath{'}}$. With adding a direct antiferromagnetic spin-exchange coupling the eigenfunctions in the particle-hole channel have extended $s$-wave form, while in the particle-particle singlet pairing channel a higher angular momentum component arises besides the standard ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave component, which flattens the angular dependence of the gap. For ${t}^{\ensuremath{'}}$ closer to $t∕2$ we find a delicate competition of ferromagnetism and triplet pairing with a nontrivial pair-wavefunction.

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Daniel Charles Mattis, Michael Dzierzawa, X. Zotos

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Physical review. B, Condensed matterOct 1, 19909 citations

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Zhu, Xing Xing, Liu +1 more

理论物理通讯：英文版Jan 1, 20010 citations

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

singlet. Odd-frequency p-wave-singlet and s-wave-triplet amplitudes are also found.

s

p

-, or

d

-wave forms, which is due to the frustration of antiferromagnetism at small and intermediate ${t}^{\ensuremath{'}}$. With adding a direct antiferromagnetic spin-exchange coupling the eigenfunctions in the particle-hole channel have extended

s

-wave form, while in the particle-particle singlet pairing channel a higher angular momentum component arises besides the standard ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ wave component, which flattens the angular dependence of the gap. For ${t}^{\ensuremath{'}}$ closer to

t∕2

we find a delicate competition of ferromagnetism and triplet pairing with a nontrivial pair-wavefunction.

The extended Hubbard model describes fermions on a lattice coupled through on-site,

U

, and first-neighbor,

V

, interactions. In the context of high-

{T}_{c}

cuprates, antiferromagnetic fluctuations may lead to an attractive channel, hence to superconductivity. Despite interest in the two-dimensional version of the model, the current knowledge about the phase diagram is still far from complete. Here, we report on the results of extensive determinant quantum Monte Carlo simulations for this model at half filling, in which we have used the average sign of the product of fermionic determinants as an additional observable to locate critical points. We arrive at a ground state phase diagram in the $U\text{\ensuremath{-}}V$ plane in which the boundaries involving antiferromagnetic, charge-ordered,

s

- and

d

-wave superconductivity, and phase-separated phases are quantitatively set with good accuracy. We have also proposed a partial phase diagram,

{T}_{c}(U,V)

, featuring critical temperatures for the charge-density wave and

s

-wave superconducting phases.

Magnetic properties of the two-dimensional Hubbard-model are inferred from results of Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8 and temperatures down to

T=\frac{t}{20}

(

t=\mathrm{hopping}

) were studied. The half-filled system is found to exhibit antiferromagnetic long-range order for all values of the Coulomb repulsion

U

. The low-temperature magnetic properties are found to be well described by spin-wave theory with renormalized local moment and spin-wave velocity. Numerical evidence presented suggests that when doped the system loses the long-range order immediately away from half filling.

{\mathit{E}}_{\mathit{g}}

and

{\mathit{m}}^{\mathrm{*}}

are found to be temperature dependent.