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arXiv:cond-mat/9310001 · Physical review. B, Condensed matter

Hole-hole contact interaction in thet-Jmodel

AL Chernyshev, A. V. Dotsenko, Oleg P. Sushkov

Published Mar 1, 1994• 26 citations
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Abstract

Using a variational approach we calculate the hole-hole contact interaction on the quantum N\'eel background. Explicit analytical expressions for the vertex function of the interaction are obtained. Solution of the Bethe-Salpeter equation with this interaction gives bound states in d and p waves with binding energies close to those obtained recently by numerical methods. At t/J\ensuremath{\ge}2--3 the bound state disappears.

DOI
10.1103/physrevb.49.6197

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Using a variational approach we calculate the hole-hole contact interaction on the quantum N'eel background. Explicit analytical expressions for the vertex function of the interaction are obtained. Solution of the Bethe-Salpeter equation with this interaction gives bound states in d and p waves with binding energies close to those obtained recently by numerical methods. At t/J\ensuremath{\ge}2--3 the bound state disappears.
The ground state of two holes with opposite spins in the t-J model is discussed using a variational method in a restricted Hilbert space. It is assumed that the holes can move independently and scatter when they are close to each other. Various processes which lead to a scattering of the holes are all treated on the same footing. It is found that the two holes form a bound state with a binding energy which is smaller than 0.4J for any value t/J. A possible extension to the case of finite concentrations is discussed.
We calculated the binding energy of two holes with antiparallel spin in the t-J model using a variational wave function based on the string or spin-bag picture. The symmetry of the bound state is dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2. Although the size of matrices to be diagonalized is only 3\ifmmode\times\else\texttimes\fi{}3 we could reproduce the results of various extensive numerical calculations with reasonable accuracy. We show that a sizeable contribution of the binding energy is due to the quantum fluctuations in the ground state of the Heisenberg antiferromagnet. In contrast to exact diagonalization results on small clusters in the thermodynamical limit the binding energy decreases rapidly with increasing t/J. A detailed discussion of the various finite-size effects in a small cluster is also included.
We investigate numerically the ground state of two holes with dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value Jc{\mathit{J}}_{\mathit{c}}Jc​\ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for JJc{\mathit{J}}_{\mathit{c}}Jc​.
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.