Quantum spin liquid in antiferromagnetic chain S=1/2 with Acoustic Phonons

A spin and phonon excitations spectrum are studied using quantum Monte Carlo method in antiferromagnetic chain with spins $S=1/2$ coupled nonadiabaticity with acoustic phonons . It is found the critical coupling exists to open gap in the triplet excitation spectrum for any phonon velocity. The phase boundaries of delocalized phonons and propagated the bound states of magnon and a phonon are calculated. It is shown that the spherical symmetry of the spin-spin correlation functions is broken . The magnetic and optical properties $CuGeO_3$ are explained without using spin-Peierls transition.