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Physical review. B, Condensed matter

Mobile holes in a two-dimensional Heisenberg antiferromagnet

Toshihiro Itoh, M. Arai, Takeo Fujiwara

Published Sep 1, 1990• 35 citations
Publisher

Abstract

Th t-t'-t''-J model is investigated by a rigorous diagonalization in a two-dimensional square lattice as large as \ensuremath{\surd}20 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}20 , which has no additional degeneracy. The ground state of one hole in the t-J model is at a momentum k near (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) with a total spin S=1/2 and that of two holes is at k=(0,0) with S=0. The hole pairing and nonclustering may be preferable for the ground state of the t-t'-t''-J model in the region of t'>0 and t''\ensuremath{\lesssim}0.

DOI
10.1103/physrevb.42.4834

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Physical review. B, Condensed matter•Apr 1, 1991•5 citations
Th t-t'-t''-J model is investigated by a rigorous diagonalization in a two-dimensional square lattice as large as \ensuremath{\surd}20 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}20 , which has no additional degeneracy. The ground state of one hole in the t-J model is at a momentum k near (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) with a total spin S=1/2 and that of two holes is at k=(0,0) with S=0. The hole pairing and nonclustering may be preferable for the ground state of the t-t'-t''-J model in the region of t'>0 and t''\ensuremath{\lesssim}0.
Using exact diagonalization techniques, we study one dynamical hole in the two-dimensional t-J and Hubbard models on a square lattice including a next-nearest-neighbor hopping t'. We present the phase diagram in the parameter space (J/t,t'/t), discussing the ground-state properties of the hole. At J=0, a crossing of levels exists at some value of t' separating a ferromagnetic from an antiferromagnetic ground state. For nonzero J, at least four different regions appear where the system behaves like an antiferromagnet or a (not fully saturated) ferromagnet. We study the quasiparticle behavior of the hole, showing that for small values of \ensuremath{\Vert}t'\ensuremath{\Vert} the previously presented string picture is still valid. We also find that, for a realistic set of parameters derived from the Cu-O Hamiltonian, the hole has momentum (\ensuremath{\pi}/2,\ensuremath{\pi}/2), suggesting an enhancement of the p-wave superconducting mode due to the second-neighbor interactions in the spin-bag picture. Results for the t-t'-U model are also discussed with conclusions similar to those of the t-t'-J model. In general we found that t'=0 is not a singular point of these models.
The ground state of a mobile vacancy in a square-lattice spin-1/2 Heisenberg antiferromagnet described by the t-J Hamiltonian is investigated numerically for an 18-site cluster. The ground state has spin 1/2, and the bottom of the vacancy band is at momentum k=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), for t/J4, which is consistent with the spin-wave perturbation theory. The structure of the spin configuration in the vicinity of the vacancy is examined using a number of correlation functions. The latter reveal the existence of a dipolar distortion of the staggered magnetization, as suggested by the semiclassical theory.
Ground state properties of two holes in the antiferromagnetic state in a square lattice are studied by using the t-J model and a variational method where the Hilbert space is restricted. It is shown that two holes are bound to each other and the ground state has d-symmetry for J/∣t∣≳ 0.18 with the momentum K = (0, 0). The binding energy of two holes is -0.7 ∼ -0.5 × J/∣t∣ and the average distance between two holes is 1.6 ∼ 1.8 × a, where a is the lattice constant, for realistic parameter values. Static correlation function Szz(Q) shows a broad peak around Q = (π/2, π/2) which originates from the motion of holes. By making use of the results for one and two holes, an effective Hamiltonian for the quasi-particles is proposed.
We have studied hole states on square lattices with 8, 10, 16, 18, and 20 sites by exactly diagonalizing the single-hole t-J model with twisted boundary conditions in the whole Brillouin zone. The bottom of the hole band is found to be extremely flat and anisotropic. The hole effective mass is highly anisotropic and enhanced in a quantum antiferromagnet. The momentum of a hole in the ground state is not located at high-symmetry points such as (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0), or (0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}). They are strongly lattice-size dependent and weakly parameter J/t (t is the hopping constant and J is the exchange constant) dependent. As the lattice size increases, the momentum of the ground state approaches the zone face center (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).
The t-J model exhibits an additional symmetry at J=2t. The irreducible representations of this symmetry include states with different quantities of holes and total spin. This leads to degeneracies between systems with differing number of holes and gives an upper bound on the ground-state energy for one- and two-hole systems of arbitrary dimension. Also, it leads to an exact result for the difference in the ground-state energy for momenta k=(0,0) and k=(\ensuremath{\pi},\ensuremath{\pi}) between the single-hole t-J model and the Heisenberg antiferromagnet in two dimensions.