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We study the S=1/2 quantum spin ladder system with the four-spin exchange,using density matrix renormalization group method and an exact diagonalizationmethod. Recently, the phase transition in this system and its universalityclass are studied. But there remain controversies whether the phase transitionis second order type or the other type and the nature of order parameter. Thereare arguments that the massless phase appears. But this does not agree with ourprevious result. Analyzing DMRG data, we try a new approach in order todetermine a phase which appears after the phase transition. We find that theedge state appears in the open boundary condition, investigating excitationenergies of states with higher magnetizations.Comment: Submitted to Phys. Rev. B, (REVTeX4

physical review. b, condensed matter

Staggered dimer order and criticality in an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math>quantum spin ladder system with four-spin exchange

Staggered dimer order and criticality in anS=12quantum spin ladder system with four-spin exchange