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Universality and quantum criticality in quasiperiodic spin chains

Author

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  • Utkarsh Agrawal

    (University of Massachusetts)

  • Sarang Gopalakrishnan

    (CUNY College of Staten Island
    The Graduate Center, CUNY)

  • Romain Vasseur

    (University of Massachusetts)

Abstract

Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems and disordered ones as well. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization-group transformation. These discrete sequences are therefore fixed points of a functional renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.

Suggested Citation

  • Utkarsh Agrawal & Sarang Gopalakrishnan & Romain Vasseur, 2020. "Universality and quantum criticality in quasiperiodic spin chains," Nature Communications, Nature, vol. 11(1), pages 1-7, December.
    • Handle: RePEc:nat:natcom:v:11:y:2020:i:1:d:10.1038_s41467-020-15760-5
    DOI: 10.1038/s41467-020-15760-5
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