Special CPM Seminar

A Haldane-like spin chain in the limit of strong anisotropy

Solomon Akaraka Owerre

Université de Montréal

We study the spin chain in the limit of large spins, in the opposite limit from Haldane, with a strong anisotropy, -K∑_i s_z,i², which makes the spins want to line up along the z axis with highest weight or lowest weight, and the usual exchange term with antiferromagnetic coupling, taken as a small perturbation, on a ring with periodic boundary conditions. The exchange interaction picks out the Néel states as those of lowest energy. For even number of spins, there are two, perfect Néel states, which mix, due to tunnelling (or equivalently, at high order of perturbation theory) to form either the symmetric or anti-symmetric superposition as the true ground state (depending on the value of the total spin). For an odd number of total spins, there is necessarily a defect in the Néel state, and hence an N fold degenerate ground state. These states also mix due to tunnelling (or equivalently again, at high order of perturbation theory) forming a band, leaving a two fold degenerate ground state, for all values of the spin.