Nonadiabatic interaction of acoustic phonons with spins <Emphasis Type="Italic">S</Emphasis>=1/2 in the two-dimensional Heisenberg model

The ground state of a two-dimensional antiferromagnet having spins S=1/2 and interacting with acoustic phonons is investigated in the nonadiabatic approximation using the quantum-mechanical Monte Carlo method. The critical parameters of the spin-phonon coupling, corresponding to the formation of bound spin-phonon excitations, crystal symmetry lowering, and the emergence of a gap in the spin excitation spectrum, as well as the antiferromagnet-quantum spin liquid transition, are determined. The orthorhombicity parameter, the sublattice magnetization, the violation of the spherical symmetry of spin-spin correlation functions, and the magnetic moment in Gd₂CuO₄ and Eu₂CuO₄ are calculated.