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arXiv:supr-con/9502003 · Physical review. B, Condensed matter

Two-hole bound states in a modifiedt-Jmodel

Michael Yu. Kuchiev, Oleg P. Sushkov

Published Nov 1, 1995• 6 citations
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Abstract

We consider a modified t-J model with the minima of single-hole dispersion at the points (0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}), (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0). It is shown that two holes in the antiferromagnetic background produce a bound state whose properties strongly differ from the states known in the unmodified t-J model. The bound state is d wave; it has four nodes on the face of the magnetic Brillouin zone. However, in the coordinate representation it looks like the usual s wave.

DOI
10.1103/physrevb.52.12977

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B. M. Elrick, Allan E. Jacobs

We report numerical results for the single-hole properties in the t-J model and the strong-coupling approximation to the Hubbard model in two dimensions. Using the hopping basis with over ${10}^{6}$ states we discuss (for an infinite system) the bandwidth, the leading Fourier coefficients in the dispersion, the band masses, and the spin-spin correlations near the hole. We compare our results with those obtained by other methods. The band minimum is found to be at (\ensuremath{\pi}/2,\ensuremath{\pi}/2) for the t-J model for 0.1\ensuremath{\le}t/J\ensuremath{\le}10, and for the strong-coupling model for 1\ensuremath{\le}t/J\ensuremath{\le}10. The bandwidth in both models is approximately 2J at large t/J, in rough agreement with loop-expansion results but in disagreement with other results. The strong-coupling bandwidth for t/J\ensuremath{\gtrsim}6 can be obtained from the t-J model by treating the three-site terms in first-order perturbation theory. The dispersion along the magnetic zone face is flat, giving a large parallel/perpendicular band mass ratio.

arXiv:cond-mat/9508038•Physical review. B, Condensed matter•Oct 1, 1995•6 citations
We consider a modified t-J model with the minima of single-hole dispersion at the points (0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}), (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0). It is shown that two holes in the antiferromagnetic background produce a bound state whose properties strongly differ from the states known in the unmodified t-J model. The bound state is d wave; it has four nodes on the face of the magnetic Brillouin zone. However, in the coordinate representation it looks like the usual s wave.
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.
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.
Clusters of the two-dimensional t-J model with two holes and up to 26 sites are diagonalized using a Lanczos algorithm. The behavior of the binding energy with system size suggests the existence of a finite critical value of J above which binding occurs in the bulk. Only the d-wave pair-field operator acting on the Heisenberg ground state has a finite overlap with the two-hole ground state for all the clusters considered. The related spectral function associated with the propagation of a d-wave (singlet) pair of holes in the antiferromagnetic background is calculated. The quasiparticle peak at the bottom of the spectrum as well as some structure appearing above the peak survive with increasing cluster size. Although no simple scaling law was found for the quasiparticle weight the data strongly suggest that this weight is finite in the bulk limit and is roughly proportional to the antiferromagnetic coupling J (for J1).
We report numerical results for the single-hole properties in the t-J model and the strong-coupling approximation to the Hubbard model in two dimensions. Using the hopping basis with over 106{10}^{6}106 states we discuss (for an infinite system) the bandwidth, the leading Fourier coefficients in the dispersion, the band masses, and the spin-spin correlations near the hole. We compare our results with those obtained by other methods. The band minimum is found to be at (\ensuremath{\pi}/2,\ensuremath{\pi}/2) for the t-J model for 0.1\ensuremath{\le}t/J\ensuremath{\le}10, and for the strong-coupling model for 1\ensuremath{\le}t/J\ensuremath{\le}10. The bandwidth in both models is approximately 2J at large t/J, in rough agreement with loop-expansion results but in disagreement with other results. The strong-coupling bandwidth for t/J\ensuremath{\gtrsim}6 can be obtained from the t-J model by treating the three-site terms in first-order perturbation theory. The dispersion along the magnetic zone face is flat, giving a large parallel/perpendicular band mass ratio.