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Title: 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.

Authors:
ORCiD logo [1];  [2];  [1]
  1. Univ. of Massachusetts, Amherst, MA (United States)
  2. City Univ. of New York (CUNY), NY (United States)
Publication Date:
Research Org.:
Univ. of Massachusetts, Amherst, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; National Science Foundation (NSF); Alfred P. Sloan Foundation
OSTI Identifier:
1617692
Grant/Contract Number:  
SC0019168; DMR-1653271
Resource Type:
Accepted Manuscript
Journal Name:
Nature Communications
Additional Journal Information:
Journal Volume: 11; Journal Issue: 1; Journal ID: ISSN 2041-1723
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Agrawal, Utkarsh, Gopalakrishnan, Sarang, and Vasseur, Romain. Universality and quantum criticality in quasiperiodic spin chains. United States: N. p., 2020. Web. doi:10.1038/s41467-020-15760-5.
Agrawal, Utkarsh, Gopalakrishnan, Sarang, & Vasseur, Romain. Universality and quantum criticality in quasiperiodic spin chains. United States. doi:https://doi.org/10.1038/s41467-020-15760-5
Agrawal, Utkarsh, Gopalakrishnan, Sarang, and Vasseur, Romain. Wed . "Universality and quantum criticality in quasiperiodic spin chains". United States. doi:https://doi.org/10.1038/s41467-020-15760-5. https://www.osti.gov/servlets/purl/1617692.
@article{osti_1617692,
title = {Universality and quantum criticality in quasiperiodic spin chains},
author = {Agrawal, Utkarsh and Gopalakrishnan, Sarang and Vasseur, Romain},
abstractNote = {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.},
doi = {10.1038/s41467-020-15760-5},
journal = {Nature Communications},
number = 1,
volume = 11,
place = {United States},
year = {2020},
month = {5}
}

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