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 $0.4\ensuremath{\le}J/t\ensuremath{\le}2.0$. 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 $J/t<{J}_c/t\ensuremath{\simeq}0.19$.