Universality and quantum criticality in quasiperiodic spin chains

Utkarsh Agrawal, Sarang Gopalakrishnan, Romain Vasseur

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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.

Original languageEnglish (US)
Article number2225
JournalNature communications
Issue number1
StatePublished - Dec 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General
  • General Physics and Astronomy
  • General Chemistry
  • General Biochemistry, Genetics and Molecular Biology


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