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Strong disorder RG approach – a short review of recent developments

Author

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  • Ferenc Iglói

    (Wigner Research Centre for Physics, Institute for Solid State Physics and Optics
    Institute of Theoretical Physics, Szeged University)

  • Cécile Monthus

    (Institut de Physique Théorique, Université Paris Saclay, CNRS, CEA)

Abstract

The strong disorder RG approach for random systems has been extended in many new directions since our previous review of 2005 [F. Igloi, C. Monthus, Phys. Rep. 412, 277 (2005)]. The aim of the present colloquium paper is thus to give an overview of these various recent developments. In the field of quantum disordered models, recent progress concern infinite disorder fixed points for short-ranged models in higher dimensions d > 1, strong disorder fixed points for long-ranged models, scaling of the entanglement entropy in critical ground-states and after quantum quenches, the RSRG-X procedure to construct the whole set excited stated and the RSRG-t procedure for the unitary dynamics in many-body-localized phases, the Floquet dynamics of periodically driven chains, the dissipative effects induced by the coupling to external baths, and Anderson Localization models. In the field of classical disordered models, new applications include the contact process for epidemic spreading, the strong disorder renormalization procedure for general master equations, the localization properties of random elastic networks, and the synchronization of interacting non-linear dissipative oscillators. Application of the method for aperiodic (or deterministic) disorder is also mentioned.

Suggested Citation

  • Ferenc Iglói & Cécile Monthus, 2018. "Strong disorder RG approach – a short review of recent developments," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(11), pages 1-25, November.
    • Handle: RePEc:spr:eurphb:v:91:y:2018:i:11:d:10.1140_epjb_e2018-90434-8
    DOI: 10.1140/epjb/e2018-90434-8
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    References listed on IDEAS

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    1. Christophe Chatelain & Dimitrios Voliotis, 2016. "Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(1), pages 1-12, January.
    2. Ahmed K. Ibrahim & Thomas Vojta, 2018. "Monte Carlo simulations of a disordered superconductor-metal quantum phase transition," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(12), pages 1-9, December.
    3. K. Kim & M.-S. Chang & S. Korenblit & R. Islam & E. E. Edwards & J. K. Freericks & G.-D. Lin & L.-M. Duan & C. Monroe, 2010. "Quantum simulation of frustrated Ising spins with trapped ions," Nature, Nature, vol. 465(7298), pages 590-593, June.
    4. Divakaran, Uma & Dutta, Amit, 2007. "Long-range connections, quantum magnets and dilute contact processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(1), pages 39-43.
    5. Christophe Chatelain & Dimitrios Voliotis, 2016. "Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(1), pages 1-12, January.
    6. Aoki, Hideo, 1982. "Decimation method of real-space renormalization for electron systems with application to random systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 114(1), pages 538-542.
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