Staggered dimer order and criticality in an S=1/2 quantum spin ladder system with four-spin exchange

We study an S=1/2 quantum-spin ladder system with four-spin cyclic exchange, using the density matrix renormalization group (DMRG) and exact diagonalization methods. Recently, the phase transition and its universality class in this system have been studied. However, controversies remain on whether the phase transition is second-order type or another type and on the nature of critical phenomena. In addition, there are several arguments concerning where the transition point is. Analyzing DMRG data, we use an approach to determine the ordered phase which appears after the phase transition. We find that the edge state appears under the open boundary condition by investigating excitation energies of states with higher magnetizations. We also estimate the correlation length and discuss the critical behavior.