Local magnetic structures induced by inhomogeneities of the lattice in $S=\frac{1}{2}$ bond-alternating chains and their response to a time-dependent magnetic field with noise

We study the effect of inhomogeneities of the lattice in the $S=1/2\mathrm{}$ bond-alternating chain by using a quantum Monte Carlo method and an exact diagonalization method. We adopt a defect in the alternating order as the inhomogeneity and we call it “bond impurity.” Local magnetic structures induced by the bond impurities are investigated both in the ground state and at very low temperatures. The local magnetic structure can be looked on as an effective $S=1/2\mathrm{}$ spin and the weakness of the interaction between the local structures causes the quasidegenerate states in the low energy. We also investigate the force acting between bond impurities and find that the force is generally attractive. We also study the dynamical property of the local magnetic structure. While the local magnetic structure behaves as an isolated $S=1/2\mathrm{}$ spin in the response to a time-dependent uniform field, it is found to be robust against the effect of noise applied at each site individually in the sweeping field.