Elementary excitations in the $\Delta$-chain

Abstract

We clarify elementary excitations in the $\Delta$-chain. They are found to be `kink'-`antikink' type domain wall excitations to the dimer singlet ground state. The characters of a kink and an antikink are quite different in this system: a kink has no excitation energy and is localized, while an antikink has a finite excitation energy and propagates. The excitation energy of a kink-antikink pair consists of a finite energy gap and a kinetic energy due to the free motion of the antikink. Variational wave functions for an antikink are studied to clarify its propagating states. All the numerical results are explained consistently based on this picture. At finite temperatures, thermally excited antikinks are moving in regions bounded by localized kinks. The origin of the low-temperature peak in the specific heat reported previously is explained and the peak position in the thermodynamic limit is estimated.