Abstract
We study spin-Peierls structural lattice instabilities for a spin-1/2 isotropic $XY$ chain with three-site interactions of $(XZX+YZY)$ type. Within the adopted adiabatic treatment we have to examine the ground-state energy or the Helmholtz free energy of the spin chain with exchange couplings varying coherently with a possible static lattice distortion pattern. Since the considered spin model can be converted into a system of noninteracting spinless fermions the required ground-state energy or the Helmholtz free energy can be calculated accurately without making any approximations. We examine rigorously several lattice distortion patterns focusing on dimerized and trimerized ones, which owe their presence to the spin-Peierls mechanism. We present phase diagrams illustrating the effect of the three-site interaction on the spin-Peierls lattice distortions. Finally we discuss some properties of the deformable spin chain in the ground state and at finite temperatures. In particular, we examine the transverse magnetization, the static transverse susceptibility and the specific heat illustrating the changes in these quantities due to lattice instabilities.
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