Polarons in quantum chains with XY exchange and Dzyaloshinsky-Moriya interaction

Abstract.

Excitations of the polaron types are investigated in the spin-1/2 quantum chain with XY exchange and Dzyaloshinsky-Moriya interaction, both coupled to acoustic vibrations of the substrate lattice. The study is carried out via Jordan-Wigner transformation with the help of which the spin chain is mapped onto a chain of spinless fermions. From the resulting effective fermion-lattice Hamiltonian, the discrete equations of motion are derived. These equations are solved in the continuum limit for self-trapped states near the bottom of the fermion spectrum interacting with long-wavelength acoustic lattice modes. The associate polaron solution, which has a pulse shape, is shown to propagate bound to the induced lattice kink distortion by translation along the chain at a constant velocity v. The pair can also experience an additional acceleration ϑ₀ when the free fermion charge is excited above its groundstate. The polaron binding energy is strongly reduced, depending quadratically on the ratio D/J of the Dzyaloshinsky-Moriya interaction strength D to the isotropic XY exchange interaction J. It is also found that polaron parameters depend only on the XY spin-lattice coupling but not on the Dzyaloshinsky-Moriya contribution.