Phase Transition and Hidden Orders of the Heisenberg Ladder Model in the Ground State

A ground-state phase transition of the antiferromagnetic Heisenberg ladder model is investigated by means of the exact-diagonalization method. A hidden-order correlation is defined for characterizing the ground state. The critical point and the exponent ν are estimated accurately with the use of the hidden-order correlation. The relevance of the resonating-valence-bond theory to the present system is also discussed by inspecting hidden orders and the elementary excitation.