Lg. Caron et S. Moukouri, DENSITY-MATRIX RENORMALIZATION-GROUP APPLIED TO THE GROUND-STATE OF THE XY SPIN-PEIERLS SYSTEM, Physical review letters, 76(21), 1996, pp. 4050-4053
We use the density matrix renormalization group (DMRG) to map out the
ground state of an XY spin chain coupled to dispersionless phonons of
frequency omega. We confirm the existence of a critical spin-phonon co
upling alpha(c) proportional to omega(0.7) for the onset of the spin g
ap bearing the signature of a Kosterlitz-Thouless transition. We also
observe a classical-quantum crossover when the spin-Peierls gap Delta
is of order omega. In the classical regime Delta > omega, the mean-fie
ld parameters are strongly renormalized by nonadiabatic corrections. T
his is the first application of the DMRG to phonons.