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Physical review. B, Condensed matter

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

Efthimios Kaxiras, Efstratios Manousakis

Published Aug 1, 1989• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.40.2596

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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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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.

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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.
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 finite-size corrections in exact diagonalization studies of the one- and two-dimensional Hubbard model can be reduced systematically by a grand-canonical integration over boundary conditions. We present results for ground-state properties of the two-dimensional (2D) Hubbard model and an evaluation of the specific heat for the 1D and 2D Hubbard model. We find the reduction of the finite-size corrections to be substantial, especially in two dimensions. \textcopyright{} 1996 The American Physical Society.