TY - JOUR
T1 - Universality and quantum criticality in quasiperiodic spin chains
AU - Agrawal, Utkarsh
AU - Gopalakrishnan, Sarang
AU - Vasseur, Romain
N1 - Funding Information:
We thank A. Chandran, P. Crowley, D. Huse, V. Khemani, and C. Laumann for stimulating discussions. We also thank S. Gazit, B. Kang, and J. Pixley for useful discussions and for sharing with us their unpublished Quantum Monte Carlo results. This work was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under Early Career Award No. DE-SC0019168 (U.A. and R.V.), the Alfred P. Sloan Foundation through a Sloan Research Fellowship (R.V.), and by NSF Grant Number DMR-1653271 (S.G.).
Publisher Copyright:
© 2020, The Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
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U2 - 10.1038/s41467-020-15760-5
DO - 10.1038/s41467-020-15760-5
M3 - Article
C2 - 32376859
AN - SCOPUS:85084328880
SN - 2041-1723
VL - 11
JO - Nature communications
JF - Nature communications
IS - 1
M1 - 2225
ER -