Candidates for the ground state of the anisotropic t- ${\mathit{J}}_{\mathit{z}}$ model at low hole doping are studied within two related lattices: the Cayley tree and the square lattice. The Cayley tree allows for the evaluation of the single hole as well as the hole-pair ground states to arbitrary precision. Threshold values for the formation of bound hole pairs appear to be similar for both lattices. We show that the main contributions to the binding of a hole pair on the Cayley tree comes from the excess number of frustrated bonds (``spinons''). Considering systems with a larger number of holes, we establish high stability of configurations with holes forming straight domain walls between nonequivalent antiferromagnetic domains. In particular, for the Cayley tree we find that domain-wall-like configurations have lower energy than separate hole pairs. For the square lattice, however, there exists at low but finite doping a parameter interval 0.18J/t0.56 where, in the ground state, holes are paired.Candidates for the ground state of the anisotropic t-${\mathit{J}}_{\mathit{z}}$ model at low hole doping are studied within two related lattices: the Cayley tree and the square lattice. The Cayley tree allows for the evaluation of the single hole as well as the hole-pair ground states to arbitrary precision. Threshold values for the formation of bound hole pairs appear to be similar for both lattices. We show that the main contributions to the binding of a hole pair on the Cayley tree comes from the excess number of frustrated bonds (``spinons''). Considering systems with a larger number of holes, we establish high stability of configurations with holes forming straight domain walls between nonequivalent antiferromagnetic domains. In particular, for the Cayley tree we find that domain-wall-like configurations have lower energy than separate hole pairs. For the square lattice, however, there exists at low but finite doping a parameter interval 0.18J/t0.56 where, in the ground state, holes are paired.

Physical review. B, Condensed matterJun 1, 199416 citations

Mobile holes in a two-dimensional Heisenberg antiferromagnet

Toshihiro Itoh, M. Arai, Takeo Fujiwara

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.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.

Physical review. B, Condensed matterSep 1, 199035 citations

An Aspect of Quantum Antiferromagnetism on a Square Lattice

Yuhei Natsume

Physics and chemistry of materials with low-dimensional structuresJan 1, 19921 citation

Dynamics of Two Holes in thet-JModel

Jun-ichiro Inoue, Sadamichi Maekawa

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.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.

Progress of Theoretical Physics SupplementJan 1, 199211 citations

Ground States of Quantum Antiferromagnets in Two Dimensions

Subir Sachdev A, Kwon Park

arXiv:cond-mat/0108214Annals of PhysicsMay 1, 2002102 citations

Candidates for the ground state of the anisotropic t-

{\mathit{J}}_{\mathit{z}}

model at low hole doping are studied within two related lattices: the Cayley tree and the square lattice. The Cayley tree allows for the evaluation of the single hole as well as the hole-pair ground states to arbitrary precision. Threshold values for the formation of bound hole pairs appear to be similar for both lattices. We show that the main contributions to the binding of a hole pair on the Cayley tree comes from the excess number of frustrated bonds (``spinons''). Considering systems with a larger number of holes, we establish high stability of configurations with holes forming straight domain walls between nonequivalent antiferromagnetic domains. In particular, for the Cayley tree we find that domain-wall-like configurations have lower energy than separate hole pairs. For the square lattice, however, there exists at low but finite doping a parameter interval 0.18J/t0.56 where, in the ground state, holes are paired.