Griffiths-McCoy singularities in random quantum spin chains: Exact results

Abstract

We consider random quantum (tight-binding, XX and Ising) spin chains in the off-critical region and study their Griffiths-McCoy singularities. These are obtained from the density of states of the low-energy excitations, which is calculated exactly by the Dyson-Schmidt method. In large finite systems the low-energy excitations are shown to follow the statistics of extremes and their distribution is given by the Fréchet form. Relation between the Dyson-Schmidt technique and the strong disorder renormalization group method is also discussed.

7 pages, accepted for publication in Phys. Rev. B

References in corpus (7)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Strong disorder RG approach of random systems
• Random-exchange quantum Heisenberg antiferromagnets on the square lattice
• Strong Griffiths singularities in random systems and their relation to extreme value statistics
• Strong disorder renormalization group study of S=1/2 Heisenberg antiferromagnet layers/bilayers with bond randomness, site dilution and dimer dilution
• Quantum disorder and Griffiths singularities in bond-diluted two-dimensional Heisenberg antiferromagnets
• Comparison between disordered quantum spin 1/2 chains

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