Quantum phase transition by cyclic four - spin exchange interaction for S = 1 / 2 two - leg spin ladder Yasushi Honda and Tsuyoshi Horiguchi

We investigate an S = 1/2 two-leg spin ladder with a cyclic four-spin exchange interaction whose interaction constant is denoted by J4, by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by Jrung and Jleg, respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet (S tot = 0) and the triplet (S tot = 1) states vanishes at J4/Jleg ≃ 0.3 for Jrung = Jleg. This result is in contrast with the fact that the S = 1/2 antiferromagnetic Heisenberg ladder, that is the case of Jrung 6= Jleg, J4 = 0, has a spin gap for all nonzero value of interchain interaction Jrung > 0. We find a larger value of the correlation length for the spin-pair correlation function than a linear size L of the system at J4/Jleg = 0.3 and Jrung = Jleg: the correlation length ξ is about 204 times of the lattice constant for L = 84 for these values of interactions. We also find that the string correlation function decays rather algebraically than exponentially at J4/Jleg = 0.3 and Jrung = Jleg. These results suggest that there is a quantum phase transition at J4/Jleg ≃ 0.3 for Jrung = Jleg. We estimate a phase boundary where the spin gap vanishes in a J4/Jleg−Jrung/Jleg plane and obtain a consistent result with that by a perturbation theory for Jrung/Jleg > 1. PACS. 05.10Cc, 73.43.Nq, 75.10.Jm