Localization of spinons in random Majumdar-Ghosh chains

Abstract

We study the effect of disorder on frustrated dimerized spin-1/2 chains at the Majumdar-Ghosh point. Using variational methods and density-matrix renormalization group approaches, we identify two localization mechanisms for spinons which are the deconfined fractional elementary excitations of these chains. The first one belongs to the Anderson localization class and dominates at the random Majumdar-Ghosh (RMG) point. There, spinons are almost independent, remain gapped, and localize in Lifshitz states whose localization length is analytically obtained. The RMG point then displays a quantum phase transition to phase of localized spinons at large disorder. The other mechanism is a random confinement mechanism which induces an effective interaction between spinons and brings the chain into a gapless and partially polarized phase for arbitrarily small disorder.

5+8 pages, 3+3 figures

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• Quantum-critical scaling properties of the two-dimensional random-singlet state
• Magnetic responses of randomly depleted spin ladders
• Spinon excitation spectra of the $J_1$-$J_2$ chain from analytical calculations in the dimer basis and exact diagonalization
• Exact dimer phase with anisotropic interaction for one dimensional magnets
• Tensor network renormalization group study of spin-1 random Heisenberg chains
• Frustration-induced quantum spin liquid behavior in the $s=$1/2 random-bond Heisenberg antiferromagnet on the zigzag chain
• Generation of chiral solitons in antiferromagnetic chains by a quantum quench