The stepped spin-Peierls phase transition in the quasi-one-dimensional spin-1/2 quantum XY-model

Using an extension of the Jordan-Wigner transformation (JWT) in two dimensions, the effects of weak interchain coupling on the spin-Peierls (SP) system is studied. The magnetic interaction is considered to be a quantum XY-interaction, and the spin-lattice distortion is treated quasiclassically. On the analogy of the stepped Peierls transition theory, we propose a stepped SP transition theory. We find that, when any finite transverse coupling J perpendicular to is introduced between nearest chains, the usual SP transition will be modified, and the dimerization and the opening of the gap will no longer occur simultaneously. This leads to the appearance of a gapless SP phase over a certain temperature region.