Universality and quantum criticality in quasiperiodic spin chains
Abstract
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.
- Publication Date:
- Research Org.:
- Univ. of Massachusetts, Amherst, MA (United States)
- Sponsoring Org.:
- USDOE; 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:
- 1781899
- Alternate Identifier(s):
- OSTI ID: 1617692
- Grant/Contract Number:
- SC0019168; DMR-1653271
- Resource Type:
- Published Article
- Journal Name:
- Nature Communications
- Additional Journal Information:
- Journal Name: Nature Communications Journal Volume: 11 Journal Issue: 1; Journal ID: ISSN 2041-1723
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United Kingdom
- 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 Kingdom: 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 Kingdom. 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 Kingdom. https://doi.org/10.1038/s41467-020-15760-5.
@article{osti_1781899,
title = {Universality and quantum criticality in quasiperiodic spin chains},
author = {Agrawal, Utkarsh and Gopalakrishnan, Sarang and Vasseur, Romain},
abstractNote = {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.},
doi = {10.1038/s41467-020-15760-5},
journal = {Nature Communications},
number = 1,
volume = 11,
place = {United Kingdom},
year = {Wed May 06 00:00:00 EDT 2020},
month = {Wed May 06 00:00:00 EDT 2020}
}
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Works referenced in this record:
Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
journal, November 1984
- Shechtman, D.; Blech, I.; Gratias, D.
- Physical Review Letters, Vol. 53, Issue 20, p. 1951-1953
Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
journal, August 2019
- Yao, Hepeng; Khoudli, Hakim; Bresque, Léa
- Physical Review Letters, Vol. 123, Issue 7
Strong disorder RG approach of random systems
journal, June 2005
- Igloi, F.; Monthus, C.
- Physics Reports, Vol. 412, Issue 5-6
Quasiperiodic GaAs-AlAs Heterostructures
journal, October 1985
- Merlin, R.; Bajema, K.; Clarke, Roy
- Physical Review Letters, Vol. 55, Issue 17
Renormalization-group study of the many-body localization transition in one dimension
journal, June 2019
- Morningstar, Alan; Huse, David A.
- Physical Review B, Vol. 99, Issue 22
Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018
- Cao, Yuan; Fatemi, Valla; Fang, Shiang
- Nature, Vol. 556, Issue 7699
Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
journal, July 2016
- Imbrie, John Z.
- Physical Review Letters, Vol. 117, Issue 2
Random and aperiodic quantum spin chains: A comparative study
journal, March 1998
- Iglói, F.; Karevski, D.; Rieger, H.
- The European Physical Journal B, Vol. 1, Issue 4
Quasiperiodic Quantum Ising Transitions in 1D
journal, April 2018
- Crowley, P. J. D.; Chandran, A.; Laumann, C. R.
- Physical Review Letters, Vol. 120, Issue 17
Quasiperiodic anisotropic XY model
journal, September 1988
- Satija, Indubala I.; Doria, Mauro M.
- Physical Review B, Vol. 38, Issue 7
Density Matrix Renormalization Group Study of the S = 1/2 Antiferromagnetic Heisenberg Chains with Quasiperiodic Exchange Modulation
journal, October 1999
- Hida, Kazuo
- Journal of the Physical Society of Japan, Vol. 68, Issue 10
Many-body localization edge in the random-field Heisenberg chain
journal, February 2015
- Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien
- Physical Review B, Vol. 91, Issue 8
Many-Body Delocalization as a Quantum Avalanche
journal, October 2018
- Thiery, Thimothée; Huveneers, François; Müller, Markus
- Physical Review Letters, Vol. 121, Issue 14
Topological nature of magnetization plateaus in periodically modulated quantum spin chains
journal, July 2014
- Hu, Haiping; Cheng, Chen; Xu, Zhihao
- Physical Review B, Vol. 90, Issue 3
Quasicrystals: A New Class of Ordered Structures
journal, December 1984
- Levine, Dov; Steinhardt, Paul Joseph
- Physical Review Letters, Vol. 53, Issue 26, p. 2477-2480
Rare-region effects and dynamics near the many-body localization transition: Rare-region effects and dynamics near the many-body localization transition
journal, January 2017
- Agarwal, Kartiek; Altman, Ehud; Demler, Eugene
- Annalen der Physik, Vol. 529, Issue 7
Random antiferromagnetic quantum spin chains
journal, August 1994
- Fisher, Daniel S.
- Physical Review B, Vol. 50, Issue 6
Quantum Spins and Quasiperiodicity: A Real Space Renormalization Group Approach
journal, January 2004
- Jagannathan, A.
- Physical Review Letters, Vol. 92, Issue 4
Many-body localization in spin chain systems with quasiperiodic fields
journal, August 2017
- Lee, Mac; Look, Thomas R.; Lim, S. P.
- Physical Review B, Vol. 96, Issue 7
Scaling Theory of Entanglement at the Many-Body Localization Transition
journal, September 2017
- Dumitrescu, Philipp T.; Vasseur, Romain; Potter, Andrew C.
- Physical Review Letters, Vol. 119, Issue 11
Non-power-law universality in one-dimensional quasicrystals
journal, October 2018
- Szabó, Attila; Schneider, Ulrich
- Physical Review B, Vol. 98, Issue 13
Many-Body Localization in a Disordered Quantum Ising Chain
journal, September 2014
- Kjäll, Jonas A.; Bardarson, Jens H.; Pollmann, Frank
- Physical Review Letters, Vol. 113, Issue 10
Many-body localization phase transition: A simplified strong-randomness approximate renormalization group
journal, June 2016
- Zhang, Liangsheng; Zhao, Bo; Devakul, Trithep
- Physical Review B, Vol. 93, Issue 22
Interacting fermions in self-similar potentials
journal, November 2001
- Vidal, Julien; Mouhanna, Dominique; Giamarchi, Thierry
- Physical Review B, Vol. 65, Issue 1
Anomalous Diffusion and Griffiths Effects Near the Many-Body Localization Transition
journal, April 2015
- Agarwal, Kartiek; Gopalakrishnan, Sarang; Knap, Michael
- Physical Review Letters, Vol. 114, Issue 16
Phase-ordering kinetics of one-dimensional nonconserved scalar systems
journal, September 1994
- Rutenberg, A. D.; Bray, A. J.
- Physical Review E, Vol. 50, Issue 3
Localization Problem in One Dimension: Mapping and Escape
journal, June 1983
- Kohmoto, Mahito; Kadanoff, Leo P.; Tang, Chao
- Physical Review Letters, Vol. 50, Issue 23
Colloquium : Many-body localization, thermalization, and entanglement
journal, May 2019
- Abanin, Dmitry A.; Altman, Ehud; Bloch, Immanuel
- Reviews of Modern Physics, Vol. 91, Issue 2
Many-body localization phase transition
journal, November 2010
- Pal, Arijeet; Huse, David A.
- Physical Review B, Vol. 82, Issue 17
Effect of random defects on the critical behaviour of Ising models
journal, May 1974
- Harris, A. B.
- Journal of Physics C: Solid State Physics, Vol. 7, Issue 9
Correlated Fermions in a One-Dimensional Quasiperiodic Potential
journal, November 1999
- Vidal, Julien; Mouhanna, Dominique; Giamarchi, Thierry
- Physical Review Letters, Vol. 83, Issue 19
Low-frequency conductivity in many-body localized systems
journal, September 2015
- Gopalakrishnan, Sarang; Müller, Markus; Khemani, Vedika
- Physical Review B, Vol. 92, Issue 10
Critical Properties of Random Quantum Potts and Clock Models
journal, April 1996
- Senthil, T.; Majumdar, Satya N.
- Physical Review Letters, Vol. 76, Issue 16
Observation of many-body localization of interacting fermions in a quasirandom optical lattice
journal, July 2015
- Schreiber, M.; Hodgman, S. S.; Bordia, P.
- Science, Vol. 349, Issue 6250
Anderson localization of a non-interacting Bose–Einstein condensate
journal, June 2008
- Roati, Giacomo; D’Errico, Chiara; Fallani, Leonardo
- Nature, Vol. 453, Issue 7197
Delocalization of a disordered bosonic system by repulsive interactions
journal, April 2010
- Deissler, B.; Zaccanti, M.; Roati, G.
- Nature Physics, Vol. 6, Issue 5
Aperiodic and correlated disorder in XY chains: exact results
journal, December 1999
- Hermisson, Joachim
- Journal of Physics A: Mathematical and General, Vol. 33, Issue 1
Critical behavior of random transverse-field Ising spin chains
journal, March 1995
- Fisher, Daniel S.
- Physical Review B, Vol. 51, Issue 10
Random Antiferromagnetic Chain
journal, November 1979
- Ma, Shang-keng; Dasgupta, Chandan; Hu, Chin-kun
- Physical Review Letters, Vol. 43, Issue 19
New Universality Class in Spin-One-Half Fibonacci Heisenberg Chains
journal, July 2004
- Hida, Kazuo
- Physical Review Letters, Vol. 93, Issue 3
Two Universality Classes for the Many-Body Localization Transition
journal, August 2017
- Khemani, Vedika; Sheng, D. N.; Huse, David A.
- Physical Review Letters, Vol. 119, Issue 7
A Classification of Critical Phenomena on Quasi-Crystals and Other Aperiodic Structures
journal, November 1993
- Luck, J. M.
- Europhysics Letters (EPL), Vol. 24, Issue 5
Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states
journal, May 2006
- Basko, D. M.; Aleiner, I. L.; Altshuler, B. L.
- Annals of Physics, Vol. 321, Issue 5
Renormalization group for a quasiperiodic Schrödinger operator
journal, January 1989
- Levitov, L. S.
- Journal de Physique, Vol. 50, Issue 7
Moire bands in twisted double-layer graphene
journal, July 2011
- Bistritzer, R.; MacDonald, A. H.
- Proceedings of the National Academy of Sciences, Vol. 108, Issue 30
Correlated insulator behaviour at half-filling in magic-angle graphene superlattices
journal, March 2018
- Cao, Yuan; Fatemi, Valla; Demir, Ahmet
- Nature, Vol. 556, Issue 7699
Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
journal, June 2016
- Vasseur, Romain; Moore, Joel E.
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6
Analytically Solvable Renormalization Group for the Many-Body Localization Transition
journal, January 2019
- Goremykina, Anna; Vasseur, Romain; Serbyn, Maksym
- Physical Review Letters, Vol. 122, Issue 4
Random transverse field Ising spin chains
journal, July 1992
- Fisher, Daniel S.
- Physical Review Letters, Vol. 69, Issue 3
Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems
journal, June 2013
- Serbyn, Maksym; Papić, Z.; Abanin, Dmitry A.
- Physical Review Letters, Vol. 110, Issue 26
Low-temperature properties of the random Heisenberg antiferromagnetic chain
journal, August 1980
- Dasgupta, Chandan; Ma, Shang-keng
- Physical Review B, Vol. 22, Issue 3
Kosterlitz-Thouless scaling at many-body localization phase transitions
journal, March 2019
- Dumitrescu, Philipp T.; Goremykina, Anna; Parameswaran, Siddharth A.
- Physical Review B, Vol. 99, Issue 9
Topological spin excitations in Harper-Heisenberg spin chains
journal, October 2019
- Lado, J. L.; Zilberberg, Oded
- Physical Review Research, Vol. 1, Issue 3
Universal Properties of Many-Body Localization Transitions in Quasiperiodic Systems
journal, November 2018
- Zhang, Shi-Xin; Yao, Hong
- Physical Review Letters, Vol. 121, Issue 20
Phenomenology of fully many-body-localized systems
journal, November 2014
- Huse, David A.; Nandkishore, Rahul; Oganesyan, Vadim
- Physical Review B, Vol. 90, Issue 17
Aperiodic quantum XXZ chains: Renormalization-group results
journal, April 2005
- Vieira, André P.
- Physical Review B, Vol. 71, Issue 13
Infinite-randomness quantum Ising critical fixed points
journal, January 2000
- Motrunich, Olexei; Mau, Siun-Chuon; Huse, David A.
- Physical Review B, Vol. 61, Issue 2
Eigenstate phase transitions and the emergence of universal dynamics in highly excited states: Eigenstate phase transitions and the emergence of universal dynamics…
journal, January 2017
- Parameswaran, S. A.; Potter, Andrew C.; Vasseur, Romain
- Annalen der Physik, Vol. 529, Issue 7