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Physical review. B, Condensed matter

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

Sanyee Tang, J. E. Hirsch

Published Aug 1, 1989• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.40.2594

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Ground state of the strong-coupling Hubbard Hamiltonian: A numerical diagonalization study

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We exactly diagonalize the effective Hamiltonian obtained from the Hubbard model in the strong-coupling limit for a two-dimensional $\sqrt{10}\ifmmode\times\else\texttimes\fi{}\sqrt{10}$ size square lattice. The effective Hamiltonian operates on a restricted Hilbert space containing only states with singly occupied sites, which makes the diagonalization possible within reasonable computational time for the above lattice. The ground-state energy and wave function are obtained for several values of the coupling ratio $\frac{t}{U}$ and the doping fraction $x$. We find three different phases in the ($x,\frac{t}{U}$) phase diagram. The first is characterized by antiferromagnetic order which extends to the longest possible distance in the 10-site system. The second and third phases are characterized by antiferromagnetic and ferromagnetic short-range correlations, respectively. We comment on the possible relevance of the results to the recently discovered high-temperature copper-oxide superconductors.

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

Efthimios Kaxiras, Efstratios Manousakis

We establish the correctness of our exact diagonalization results for the ground state of the effective strong-coupling Hubbard Hamiltonian, and the consistency of their interpretation within the finite-size system studied. We discuss why comparison of our results to calculations by S. Tang and J. E. Hirsch (preceding Comment) is misleading and inconclusive. The possible importance of finite-size effects has already been pointed out.

Physical review. B, Condensed matter•Aug 1, 1989•0 citations

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Xin-Zhong 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 ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is the predominant one in the doped Hubbard model. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Feb 15, 1996•0 citations

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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, 1996•0 citations
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.
We exactly diagonalize the effective Hamiltonian obtained from the Hubbard model in the strong-coupling limit for a two-dimensional $\sqrt{10}\ifmmode\times\else\texttimes\fi{}\sqrt{10}$ size square lattice. The effective Hamiltonian operates on a restricted Hilbert space containing only states with singly occupied sites, which makes the diagonalization possible within reasonable computational time for the above lattice. The ground-state energy and wave function are obtained for several values of the coupling ratio tU\frac{t}{U}Ut​ and the doping fraction xxx. We find three different phases in the (x,tUx,\frac{t}{U}x,Ut​) phase diagram. The first is characterized by antiferromagnetic order which extends to the longest possible distance in the 10-site system. The second and third phases are characterized by antiferromagnetic and ferromagnetic short-range correlations, respectively. We comment on the possible relevance of the results to the recently discovered high-temperature copper-oxide superconductors.
The observed magnetic spin susceptibility of high-temperature superconductors such as ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​ increases when x increases from zero, i.e., as one dopes away from half-filling. Recent Monte Carlo simulations of A. Moreo [Phys. Rev. B 48, 3380 (1993)] suggest that this behavior can be reproduced by the two-dimensional Hubbard model only at large coupling, namely, U/t of order 10. Using longer runs, our Monte Carlo simulations show that the same behavior as for U/t=10 is obtained even in the intermediate coupling regime (U/t=4), as long as the temperature is low enough (T=t/6) that strong antiferromagnetic correlations are building up at half-filling. These results are consistent with the fact that in two dimensions, the generalized random phase approximation should fail in the parameter range where it predicts a magnetic phase transition.
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.