Physical review. B, Condensed matter

Comment on ‘‘Constraints on pairings in the Hubbard model’’

Xin-Zhong Yan

Published Feb 15, 1996• 0 citations

Abstract

We show that Shi's conclusion about the singlet pairing in the Hubbard model at strong-coupling limit [Phys. Rev. B 51, 16 619 (1995)] is wrong. The singlet pairing is related to many-particle correlated pairings. There generally is no exact identity among the singlet pairing functions. We give an intuitive argument that the nearest-neighbor ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is the predominant one in the doped Hubbard model. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physrevb.53.5024

Related papers

Constraints on pairings in the Hubbard model - Comment

XZ Yan

We show that Shi's conclusion about the singlet pairing in the Hubbard model at strong-coupling limit [Phys. Rev. B 51, 16 619 (1995)] is wrong. The singlet pairing is related to many-particle correlated pairings. There generally is no exact identity among the singlet pairing functions. We give an intuitive argument that the nearest-neighbor d(x2-y2)-wave pairing is the predominant one in the doped Hubbard model.

Jan 1, 19960 citations

Comment on ‘‘Odd-parity singlet pairing in the positive-U Hubbard model’’

Elbio R. Dagotto, A. P. Kampf, J. R. Schrieffer

A Comment on the Letter by R. Scalettar, R. R. P. Singh, and S. C. Zhang, Phys. Rev. Lett. 67, 370 (1991).Received 28 June 1991DOI:https://doi.org/10.1103/PhysRevLett.67.2918©1991 American Physical Society

Physical Review LettersNov 1, 19915 citations

Constraints on pairings in the Hubbard model

Yu Shi

Physical review. B, Condensed matterJun 15, 19952 citations

Pairing Correlations in the Two-Dimensional Hubbard Model [Phys. Rev. Lett. 78, 4486 (1997)]

Shiwei Zhang, Joseph Carlson, James E. Gubernatis

Physical Review LettersMar 13, 20002 citations

Comment on ‘‘Ground state of the strong-coupling Hubbard Hamiltonian: A numerical diagonalization study’’

Sanyee Tang, J. E. Hirsch

The interpretation of Kaxiras and Manousakis [Phys. Rev. B 37, 656 (1988)] of the data in Fig. 3 of their paper (staggered magnetization distribution) is questioned. It is argued that the existence of magnetic order in the doped Hubbard model cannot be inferred from those data, nor from the behavior of short-range spin-correlation functions.

Physical review. B, Condensed matterAug 1, 19892 citations

Comment on ‘‘New 1/Nexpansion method for the generalized Hubbard model’’

P. G. J. van Dongen

Physical Review LettersNov 9, 19922 citations

Physical review. B, Condensed matter

Comment on ‘‘Constraints on pairings in the Hubbard model’’

Xin-Zhong Yan

Published Feb 15, 1996• 0 citations

Publisher

Abstract

{\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}

-wave pairing is the predominant one in the doped Hubbard model. \textcopyright{} 1996 The American Physical Society.

DOI: 10.1103/physrevb.53.5024

Related papers

Constraints on pairings in the Hubbard model - Comment

XZ Yan

We show that Shi's conclusion about the singlet pairing in the Hubbard model at strong-coupling limit [Phys. Rev. B 51, 16 619 (1995)] is wrong. The singlet pairing is related to many-particle correlated pairings. There generally is no exact identity among the singlet pairing functions. We give an intuitive argument that the nearest-neighbor d(x2-y2)-wave pairing is the predominant one in the doped Hubbard model.

Jan 1, 19960 citations

Comment on ‘‘Odd-parity singlet pairing in the positive-U Hubbard model’’

Elbio R. Dagotto, A. P. Kampf, J. R. Schrieffer

Physical Review LettersNov 1, 19915 citations

Constraints on pairings in the Hubbard model

Yu Shi

Pairing operators of electrons with an arbitrary distance on a square lattice are defined in each possible wave channel, s, p, ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ , ${\mathit{d}}_{\mathit{x}\mathit{y}}$ , and ${\mathit{g}}_{\mathit{x}}^{3}$ y- ${\mathit{xy}}^{3}$ . Exact identities among pairing amplitudes in the Hubbard model are presented, giving powerful constraints on the nature of pairings. At half filling, some of the pairing amplitudes, including those of the second-shortest pairing distance, vanish identically in each wave channel except the p wave. There are correlations among pairing amplitudes away from half filling, as well as nonidentically vanishing ones at half filling. Even if the pairing amplitudes vanish up to a certain distance, those of larger distances can still possibly be nonzero. The order of magnitude is estimated for the pairine amplitudes, indicating that those of large distances can by no means be neglected. The scheme is also used in the extended Hubbard model including nearest-neighbor density-density interaction and that including next-nearest-neighbor hopping. In that including nearest-neighbor interaction, the features of pairing amplitudes are just the same as in the original Hubbard model at half filling, and are also similar away from half filling, but with the difference that the amplitude is now dependent on the nearest-neighbor interaction. In the model including next-nearest-neighbor hopping, the features are quite different, the constraint identities are more underconstrained, and the amplitude has no monotonic dependence upon the pairing distance if the next-nearest-neighbor hopping has an opposite sign to the nearest-neighbor hopping as required physically. The same scheme is also used to discuss the possible pairings in the coupled two-plane Hubbard model and in the infinite-layer Hubbard model.Pairing operators of electrons with an arbitrary distance on a square lattice are defined in each possible wave channel, s, p, ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$, ${\mathit{d}}_{\mathit{x}\mathit{y}}$, and ${\mathit{g}}_{\mathit{x}}^{3}$y-${\mathit{xy}}^{3}$. Exact identities among pairing amplitudes in the Hubbard model are presented, giving powerful constraints on the nature of pairings. At half filling, some of the pairing amplitudes, including those of the second-shortest pairing distance, vanish identically in each wave channel except the p wave. There are correlations among pairing amplitudes away from half filling, as well as nonidentically vanishing ones at half filling. Even if the pairing amplitudes vanish up to a certain distance, those of larger distances can still possibly be nonzero. The order of magnitude is estimated for the pairine amplitudes, indicating that those of large distances can by no means be neglected. The scheme is also used in the extended Hubbard model including nearest-neighbor density-density interaction and that including next-nearest-neighbor hopping. In that including nearest-neighbor interaction, the features of pairing amplitudes are just the same as in the original Hubbard model at half filling, and are also similar away from half filling, but with the difference that the amplitude is now dependent on the nearest-neighbor interaction. In the model including next-nearest-neighbor hopping, the features are quite different, the constraint identities are more underconstrained, and the amplitude has no monotonic dependence upon the pairing distance if the next-nearest-neighbor hopping has an opposite sign to the nearest-neighbor hopping as required physically. The same scheme is also used to discuss the possible pairings in the coupled two-plane Hubbard model and in the infinite-layer Hubbard model.

Physical review. B, Condensed matterJun 15, 19952 citations

Pairing Correlations in the Two-Dimensional Hubbard Model [Phys. Rev. Lett. 78, 4486 (1997)]

Shiwei Zhang, Joseph Carlson, James E. Gubernatis

Physical Review LettersMar 13, 20002 citations

Comment on ‘‘Ground state of the strong-coupling Hubbard Hamiltonian: A numerical diagonalization study’’

Sanyee Tang, J. E. Hirsch

Physical review. B, Condensed matterAug 1, 19892 citations

Comment on ‘‘New 1/Nexpansion method for the generalized Hubbard model’’

P. G. J. van Dongen

Physical Review LettersNov 9, 19922 citations

{\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}

-wave pairing is the predominant one in the doped Hubbard model. \textcopyright{} 1996 The American Physical Society.

Pairing operators of electrons with an arbitrary distance on a square lattice are defined in each possible wave channel, s, p,

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

{\mathit{y}}^{2}

{\mathit{d}}_{\mathit{x}\mathit{y}}

, and

{\mathit{g}}_{\mathit{x}}^{3}

{\mathit{xy}}^{3}

. Exact identities among pairing amplitudes in the Hubbard model are presented, giving powerful constraints on the nature of pairings. At half filling, some of the pairing amplitudes, including those of the second-shortest pairing distance, vanish identically in each wave channel except the p wave. There are correlations among pairing amplitudes away from half filling, as well as nonidentically vanishing ones at half filling. Even if the pairing amplitudes vanish up to a certain distance, those of larger distances can still possibly be nonzero. The order of magnitude is estimated for the pairine amplitudes, indicating that those of large distances can by no means be neglected. The scheme is also used in the extended Hubbard model including nearest-neighbor density-density interaction and that including next-nearest-neighbor hopping. In that including nearest-neighbor interaction, the features of pairing amplitudes are just the same as in the original Hubbard model at half filling, and are also similar away from half filling, but with the difference that the amplitude is now dependent on the nearest-neighbor interaction. In the model including next-nearest-neighbor hopping, the features are quite different, the constraint identities are more underconstrained, and the amplitude has no monotonic dependence upon the pairing distance if the next-nearest-neighbor hopping has an opposite sign to the nearest-neighbor hopping as required physically. The same scheme is also used to discuss the possible pairings in the coupled two-plane Hubbard model and in the infinite-layer Hubbard model.