Spinon excitations in 2D quantum spin liquid with S=1/2 interacting with acoustic phonons

Spin density of states in the spin-1/2 two-dimensional antiferromagnet interacting with acoustic phonons in a magnetic field is calculated using the quantum Monte Carlo method. It is found the gap A in the single-particle spin-excitation spectrum closes at magnetic fields Delta similar or equal to H-c, W-ph < W-s and Delta similar or equal to (1/2)H-c, W-ph > W-s, where W-ph and W-s are the bandwidths of phonon and spin excitations in an antiferromagnet.