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Universality and quantum criticality in quasiperiodic spin chains.

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.

SUBMITTER: Agrawal U

PROVIDER: S-EPMC7203221 | biostudies-literature | 2020 May

REPOSITORIES: biostudies-literature

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Universality and quantum criticality in quasiperiodic spin chains.

Agrawal Utkarsh U Gopalakrishnan Sarang S Vasseur Romain R

Nature communications 20200506 1

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 tr ...[more]

PMID: 32376859

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