Anisotropy-induced spin parity effect in an antiferromagnetic spin chain

Spin parity effects — physics which alters between integer and half-odd integer spin cases — often manifest themselves in quantum spin systems, perhaps the most prominent example being the Haldane conjecture for one-dimensional antiferromagnets. In this study we discuss a new and very general mechanism by which spin parity effects can emerge, through the detailed study of an antiferromagnetic spin chain that possesses a spin-ion anisotropy and is subjected to a transverse magnetic field. Using numerical exact diagonalization, we examine the manner in which the ground state undergoes a series of level crossings upon sweeping the magnetic field, between states with crystal momenta 0 and π. We find that such level crossings disappear in integer-spin systems when the anisotropy becomes large, whereas they are robustly present in the case of half-odd integer spins. These results are attributed to the quantitative difference in the nature of the excitation gap in the thermodynamic limit for the two cases, which can be understood in terms of Tomonaga–Luttinger liquid notions, augmented with perturbation theory, as well as with field theory. We will point out how the anisotropy-induced spin parity effect we discovered can be extended to higher-dimensional spin systems.