The spin-Peierls instability in spin 1/2 XY chain in the non adiabatic   limit
  The spin-Peierls instability in spin 1/2 XY chain coupled to dispersionless phonons of frequency $\omega$ has been studied in the nonadiabatic limit. We have chosen the Lang-Firsov variational wave function for the phonon subsystem to obtain an effective spin Hamiltonian. The effective spin Hamiltonian is then solved in the framework of mean-field approximation. We observed a dimerized phase when g is less than a critical value and an anti-ferromagnetic phase when it is greater than a critical value . The variation of lattice distortion, dimerized order parameter and energy gap with spin phonon coupling parameter has also been investigated here. 
Shreekantha Sil (Theo. Phys., Univ. Koln, Germany)