Strong disorder renormalization group study of S=1/2 Heisenberg antiferromagnet layers/bilayers with bond randomness, site dilution and dimer dilution

Abstract

Using a numerical implementation of strong disorder renormalization group, we study the low-energy, long-distance properties of layers and bilayers of $S=1/2$ Heisenberg antiferromagnets with different type of disorder: bond randomness, site and dimer dilution. Generally the systems exhibit an ordered and a disordered phase separated by a phase boundary on which the static critical exponents appear to be independent of bond randomness in the strong disorder regime, while the dynamical exponent is a continuous function of the bond disorder strength. The low-energy fixed points of the off-critical phases are affected by the actual form of the disorder, and the disorder induced dynamical exponent depends on the disorder strength. As the strength of bond disorder is increased, there is a set of crossovers in the properties of the low-energy singularities. For weak disorder quantum fluctuations play the dominant role. For intermediate disorder non-localized disorder fluctuations are relevant, which become localized for even stronger bond disorder. We also present some quantum Monte Carlo simulations results to support the strong disorder renormalization approach.

arXiv comment12 pages, 13 figures

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• Nature of the low-energy excitations of two-dimensional diluted Heisenberg quantum antiferromagnets
• Long-range random transverse-field Ising model in three dimensions
• Griffiths Singularities in the Random Quantum Ising Antiferromagnet: A Tree Tensor Network Renormalization Group Study
• Excitation spectra of disordered dimer magnets near quantum criticality
• Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters
• Long-range epidemic spreading in a random environment
• Quantum-critical scaling properties of the two-dimensional random-singlet state
• Tensor network renormalization group study of spin-1 random Heisenberg chains
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