Thermodynamic properties of the two-dimensional $S=\frac{1}{2}$ Heisenberg antiferromagnet coupled to bond phonons

By applying a quantum Monte Carlo procedure based on the loop algorithm we investigate thermodynamic properties of the two-dimensional antiferromagnetic $S=\frac{1}{2}$ Heisenberg model coupled to Einstein phonons on the bonds. The temperature dependence of the magnetic susceptibility, mean phonon occupation numbers, and the specific heat are discussed in detail. We study the spin-correlation function both in the regime of weak and strong spin phonon coupling (coupling constants $g=0.1,$ $\omega =8J$ and $g=2,$ $\omega =2J,$ respectively). A finite-size scaling analysis of the correlation length indicates that in both cases long-range Néel order is established in the ground state.