Localization of spinons in random Majumdar-Ghosh chains

We study the effect of disorder on frustrated dimerized spin-1/2 chains at the Majumdar-Ghosh point. The Majumdar-Ghosh condition is first generalized in the presence of random bonds, defining a random Majumdar-Ghosh (RMG) point with locally correlated disorder. Using variational methods and density-matrix renormalization group approaches, we show that spinons, the deconfined fractional elementary excitations of the chains, remain gapped at the RMG point but get localized in Lifshitz states whose localization length is analytically obtained. Increasing the disorder strength at the RMG point induces a transition to a paramagnetic phase of localized spinons. Moving away from the RMG point by uncorrelating the random bonds, an effective interaction between spinons brings the chain into a gapless and partially polarized phase for arbitrarily small disorder.