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Two holes in a two-dimensional quantum antiferromagnet: A variational study based on entangled-plaquette states

We show that the entangled-plaquette variational ansatz can be adapted to study the two-dimensional $t-J$ model in the presence of two mobile holes. Specifically, we focus on a square lattice comprising up to $N=256$ sites in the parameter range $0.4\leq J/ t\leq2.0$. Ground state energies are obtained via the optimization of a wave function in which the weight of a given configuration is expressed in terms of variational coefficients associated with square and linear entangled plaquettes. Our estimates are in excellent agreement with exact results available for the $N=16$ lattice. By extending our study to considerably larger systems we find, based on the analysis of the long distance tail of the probability of finding two holes at spatial separation $r$, and on our computed two-hole binding energies, the existence of a two-hole bound state for all the values of $J/t$ explored here. It is estimated that d-wave binding of the two holes does not occur for $J/t<J_c/t\simeq 0.19$.