Groundstate Properties of Frustrated Spin Systems on a Ladder

Abstract

A spin-1/2 Heisenberg model on a ladder, which consists of one ferromagnetic leg and one antiferromagnetic leg connected by antiferromagnetic rungs, is discussed. The phase transition in the groundstate is investigated in such a system. It is shown that the spontaneous magnetization, m , becomes zero if the interchain coupling R is larger than a critical value R c . It is found that R c =1.134461 ±0.000001 by the exact diagonalization. In the region R < R c , we also find that the spontaneous magnetization is proportional to \(\sqrt{R_{\rm c}-R}\) near the critical point R c . Moreover an exact eigenstate with the total spin S =0 is obtained.