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Dimerized antiferromagnetic spin-1/2 ladders are known to exhibit a quantumcritical phase transition in the ground state, the existence or absence ofwhich is dependent on the dimerization pattern of the ladder. The gapped phasescannot be distinguished by the conventional Landau long-range order parameter.However, they possess a non-local (hidden) string order parameter, which isnon-zero in one phase and vanishes in the other. We use an exactdiagonalization technique to calculate ground state energies, energy gaps andstring order parameters of dimerized two- and three-leg Heisenberg ladders, aswell as a critical scaling analysis to yield estimates of the criticalexponents nu and beta.

Numerical study of critical properties and hidden orders in dimerized spin ladders