From tunnels to towers: Quantum scars from Lie algebras and -deformed Lie algebras
Abstract
We present a general symmetry-based framework for obtaining many-body Hamiltonians with scarred eigenstates that do not obey the eigenstate thermalization hypothesis. Our models are derived from parent Hamiltonians with a non-Abelian (or q-deformed) symmetry, whose eigenspectra are organized as degenerate multiplets that transform as irreducible representations of the symmetry (`tunnels'). We show that large classes of perturbations break the symmetry, but in a manner that preserves a particular low-entanglement multiplet of states -- thereby giving generic, thermal spectra with a `shadow' of the broken symmetry in the form of scars. The generators of the Lie algebra furnish operators with `spectrum generating algebras' that can be used to lift the degeneracy of the scar states and promote them to equally spaced `towers'. Our framework applies to several known models with scars, but we also introduce new models with scars that transform as irreducible representations of symmetries such as SU(3) and q-deformed SU(2), significantly generalizing the types of systems known to harbor this phenomenon. Additionally, we present new examples of generalized AKLT models with scar states that do not transform in an irreducible representation of the relevant symmetry. These are derived from parent Hamiltonians with enhanced symmetries, and bring AKLT-like models intomore »
- Authors:
- Publication Date:
- Research Org.:
- Stanford Univ., CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR)
- OSTI Identifier:
- 1730971
- Alternate Identifier(s):
- OSTI ID: 1785237
- Grant/Contract Number:
- SC0021111; DMR-1752759; DMR-1928166; FA9550-20-1-0235
- Resource Type:
- Published Article
- Journal Name:
- Physical Review Research
- Additional Journal Information:
- Journal Name: Physical Review Research Journal Volume: 2 Journal Issue: 4; Journal ID: ISSN 2643-1564
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 74 ATOMIC AND MOLECULAR PHYSICS
Citation Formats
O'Dea, Nicholas, Burnell, Fiona, Chandran, Anushya, and Khemani, Vedika. From tunnels to towers: Quantum scars from Lie algebras and q -deformed Lie algebras. United States: N. p., 2020.
Web. doi:10.1103/PhysRevResearch.2.043305.
O'Dea, Nicholas, Burnell, Fiona, Chandran, Anushya, & Khemani, Vedika. From tunnels to towers: Quantum scars from Lie algebras and q -deformed Lie algebras. United States. https://doi.org/10.1103/PhysRevResearch.2.043305
O'Dea, Nicholas, Burnell, Fiona, Chandran, Anushya, and Khemani, Vedika. Wed .
"From tunnels to towers: Quantum scars from Lie algebras and q -deformed Lie algebras". United States. https://doi.org/10.1103/PhysRevResearch.2.043305.
@article{osti_1730971,
title = {From tunnels to towers: Quantum scars from Lie algebras and q -deformed Lie algebras},
author = {O'Dea, Nicholas and Burnell, Fiona and Chandran, Anushya and Khemani, Vedika},
abstractNote = {We present a general symmetry-based framework for obtaining many-body Hamiltonians with scarred eigenstates that do not obey the eigenstate thermalization hypothesis. Our models are derived from parent Hamiltonians with a non-Abelian (or q-deformed) symmetry, whose eigenspectra are organized as degenerate multiplets that transform as irreducible representations of the symmetry (`tunnels'). We show that large classes of perturbations break the symmetry, but in a manner that preserves a particular low-entanglement multiplet of states -- thereby giving generic, thermal spectra with a `shadow' of the broken symmetry in the form of scars. The generators of the Lie algebra furnish operators with `spectrum generating algebras' that can be used to lift the degeneracy of the scar states and promote them to equally spaced `towers'. Our framework applies to several known models with scars, but we also introduce new models with scars that transform as irreducible representations of symmetries such as SU(3) and q-deformed SU(2), significantly generalizing the types of systems known to harbor this phenomenon. Additionally, we present new examples of generalized AKLT models with scar states that do not transform in an irreducible representation of the relevant symmetry. These are derived from parent Hamiltonians with enhanced symmetries, and bring AKLT-like models into our framework.},
doi = {10.1103/PhysRevResearch.2.043305},
journal = {Physical Review Research},
number = 4,
volume = 2,
place = {United States},
year = {2020},
month = {12}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevResearch.2.043305
https://doi.org/10.1103/PhysRevResearch.2.043305
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Local Conservation Laws and the Structure of the Many-Body Localized States
journal, September 2013
- Serbyn, Maksym; Papić, Z.; Abanin, Dmitry A.
- Physical Review Letters, Vol. 111, Issue 12
Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain
journal, April 2019
- Lin, Cheng-Ju; Motrunich, Olexei I.
- Physical Review Letters, Vol. 122, Issue 17
The spectra of q-state vertex models and related antiferromagnetic quantum spin chains
journal, March 1990
- Klumper, A.
- Journal of Physics A: Mathematical and General, Vol. 23, Issue 5
Rigorous results on valence-bond ground states in antiferromagnets
journal, August 1987
- Affleck, Ian; Kennedy, Tom; Lieb, Elliott H.
- Physical Review Letters, Vol. 59, Issue 7
Thermalization and its mechanism for generic isolated quantum systems
journal, April 2008
- Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim
- Nature, Vol. 452, Issue 7189
Quasitriangular hopf Algebras and Yang-Baxter Equations
journal, January 1990
- Majid, Shahn
- International Journal of Modern Physics A, Vol. 05, Issue 01
Statistical Behavior in Deterministic Quantum Systems with Few Degrees of Freedom
journal, April 1985
- Jensen, R. V.; Shankar, R.
- Physical Review Letters, Vol. 54, Issue 17
Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension
journal, January 2017
- Vafek, Oskar; Regnault, Nicolas; Bernevig, B. Andrei
- SciPost Physics, Vol. 3, Issue 6
Spin-s quantum chains and Temperley-Lieb algebras
journal, January 1990
- Batchelor, M. T.; Barber, M. N.
- Journal of Physics A: Mathematical and General, Vol. 23, Issue 1
-pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars
journal, August 2020
- Moudgalya, Sanjay; Regnault, Nicolas; Bernevig, B. Andrei
- Physical Review B, Vol. 102, Issue 8
Quasilocal conservation laws from semicyclic irreducible representations of in XXZ spin-1/2 chains
journal, January 2016
- Zadnik, Lenart; Medenjak, Marko; Prosen, Tomaž
- Nuclear Physics B, Vol. 902
Emergent SU(2) Dynamics and Perfect Quantum Many-Body Scars
journal, June 2019
- Choi, Soonwon; Turner, Christopher J.; Pichler, Hannes
- Physical Review Letters, Vol. 122, Issue 22
Slow thermalization of exact quantum many-body scar states under perturbations
journal, July 2020
- Lin, Cheng-Ju; Chandran, Anushya; Motrunich, Olexei I.
- Physical Review Research, Vol. 2, Issue 3
Nonthermal States Arising from Confinement in One and Two Dimensions
journal, April 2019
- James, Andrew J. A.; Konik, Robert M.; Robinson, Neil J.
- Physical Review Letters, Vol. 122, Issue 13
Lattice Gauge Theories and String Dynamics in Rydberg Atom Quantum Simulators
journal, May 2020
- Surace, Federica M.; Mazza, Paolo P.; Giudici, Giuliano
- Physical Review X, Vol. 10, Issue 2
Onsager’s Scars in Disordered Spin Chains
journal, May 2020
- Shibata, Naoyuki; Yoshioka, Nobuyuki; Katsura, Hosho
- Physical Review Letters, Vol. 124, Issue 18
η pairing and off-diagonal long-range order in a Hubbard model
journal, November 1989
- Yang, Chen Ning
- Physical Review Letters, Vol. 63, Issue 19
Exact excited states of nonintegrable models
journal, December 2018
- Moudgalya, Sanjay; Rachel, Stephan; Bernevig, B. Andrei
- Physical Review B, Vol. 98, Issue 23
Quantum many-body scars from magnon condensation
journal, November 2019
- Iadecola, Thomas; Schecter, Michael; Xu, Shenglong
- Physical Review B, Vol. 100, Issue 18
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians
journal, February 2020
- Sala, Pablo; Rakovszky, Tibor; Verresen, Ruben
- Physical Review X, Vol. 10, Issue 1
Probing many-body dynamics on a 51-atom quantum simulator
journal, November 2017
- Bernien, Hannes; Schwartz, Sylvain; Keesling, Alexander
- Nature, Vol. 551, Issue 7682
Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 Magnets
journal, October 2019
- Schecter, Michael; Iadecola, Thomas
- Physical Review Letters, Vol. 123, Issue 14
Topological many-body scar states in dimensions one, two, and three
journal, December 2019
- Ok, Seulgi; Choo, Kenny; Mudry, Christopher
- Physical Review Research, Vol. 1, Issue 3
Class of exactly solvable symmetric spin chains with matrix product ground states
journal, September 2008
- Tu, Hong-Hao; Zhang, Guang-Ming; Xiang, Tao
- Physical Review B, Vol. 78, Issue 9
Hidden symmetry breaking and the Haldane phase inS=1 quantum spin chains
journal, July 1992
- Kennedy, Tom; Tasaki, Hal
- Communications in Mathematical Physics, Vol. 147, Issue 3
Onsager symmetries in $U(1)$ -invariant clock models
journal, April 2019
- Vernier, Eric; O’Brien, Edward; Fendley, Paul
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, Issue 4
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
Quantum East Model: Localization, Nonthermal Eigenstates, and Slow Dynamics
journal, June 2020
- Pancotti, Nicola; Giudice, Giacomo; Cirac, J. Ignacio
- Physical Review X, Vol. 10, Issue 2
Large classes of quantum scarred Hamiltonians from matrix product states
journal, August 2020
- Moudgalya, Sanjay; O'Brien, Edward; Bernevig, B. Andrei
- Physical Review B, Vol. 102, Issue 8
Unified structure for exact towers of scar states in the Affleck-Kennedy-Lieb-Tasaki and other models
journal, May 2020
- Mark, Daniel K.; Lin, Cheng-Ju; Motrunich, Olexei I.
- Physical Review B, Vol. 101, Issue 19
Symmetry-protected topological phases beyond groups: The -deformed Affleck-Kennedy-Lieb-Tasaki model
journal, August 2020
- Quella, Thomas
- Physical Review B, Vol. 102, Issue 8
Determining a local Hamiltonian from a single eigenstate
journal, July 2019
- Qi, Xiao-Liang; Ranard, Daniel
- Quantum, Vol. 3
q-deformations of the O(3) symmetric spin-1 Heisenberg chain
journal, February 1990
- Batchelor, M. T.; Mezincescu, L.; Nepomechie, R. I.
- Journal of Physics A: Mathematical and General, Vol. 23, Issue 4
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
journal, May 2016
- D'Alessio, Luca; Kafri, Yariv; Polkovnikov, Anatoli
- Advances in Physics, Vol. 65, Issue 3
Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis
journal, December 2018
- Moudgalya, Sanjay; Regnault, Nicolas; Bernevig, B. Andrei
- Physical Review B, Vol. 98, Issue 23
Slow Quantum Thermalization and Many-Body Revivals from Mixed Phase Space
journal, March 2020
- Michailidis, A. A.; Turner, C. J.; Papić, Z.
- Physical Review X, Vol. 10, Issue 1
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
Groundstate properties of a generalized VBS-model
journal, October 1992
- Kl�mper, A.; Schadschneider, A.; Zittartz, J.
- Zeitschrift f�r Physik B Condensed Matter, Vol. 87, Issue 3
Isolated Heisenberg magnet as a quantum time crystal
journal, July 2020
- Medenjak, Marko; Buča, Berislav; Jaksch, Dieter
- Physical Review B, Vol. 102, Issue 4
Periodic Orbits, Entanglement, and Quantum Many-Body Scars in Constrained Models: Matrix Product State Approach
journal, January 2019
- Ho, Wen Wei; Choi, Soonwon; Pichler, Hannes
- Physical Review Letters, Vol. 122, Issue 4
Weak ergodicity breaking from quantum many-body scars
journal, May 2018
- Turner, C. J.; Michailidis, A. A.; Abanin, D. A.
- Nature Physics, Vol. 14, Issue 7
The matrix product representation for the q-VBS state of one-dimensional higher integer spin model
journal, July 2010
- Motegi, Kohei
- Physics Letters A, Vol. 374, Issue 31-32
Localization from Hilbert space shattering: From theory to physical realizations
journal, May 2020
- Khemani, Vedika; Hermele, Michael; Nandkishore, Rahul
- Physical Review B, Vol. 101, Issue 17
Many-Body Localization and Thermalization in Quantum Statistical Mechanics
journal, March 2015
- Nandkishore, Rahul; Huse, David A.
- Annual Review of Condensed Matter Physics, Vol. 6, Issue 1
Entanglement spectra of q -deformed higher spin VBS states
journal, April 2012
- Santos, Raul A.; Paraan, Francis N. C.; Korepin, Vladimir E.
- Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 17
-pairing states as true scars in an extended Hubbard model
journal, August 2020
- Mark, Daniel K.; Motrunich, Olexei I.
- Physical Review B, Vol. 102, Issue 7
Quantum statistical mechanics in a closed system
journal, February 1991
- Deutsch, J. M.
- Physical Review A, Vol. 43, Issue 4
Chaos and quantum thermalization
journal, August 1994
- Srednicki, Mark
- Physical Review E, Vol. 50, Issue 2
Quantum scars as embeddings of weakly broken Lie algebra representations
journal, April 2020
- Bull, Kieran; Desaules, Jean-Yves; Papić, Zlatko
- Physical Review B, Vol. 101, Issue 16
Phenomenology of fully many-body-localized systems
journal, November 2014
- Huse, David A.; Nandkishore, Rahul; Oganesyan, Vadim
- Physical Review B, Vol. 90, Issue 17
Hidden symmetry breaking in a generalized valence-bond solid model
journal, October 1994
- Totsuka, K.; Suzuki, M.
- Journal of Physics A: Mathematical and General, Vol. 27, Issue 19
Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis
journal, July 2017
- Shiraishi, Naoto; Mori, Takashi
- Physical Review Letters, Vol. 119, Issue 3
Symmetry protection of topological phases in one-dimensional quantum spin systems
journal, February 2012
- Pollmann, Frank; Berg, Erez; Turner, Ari M.
- Physical Review B, Vol. 85, Issue 7
Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
journal, December 2010
- Biroli, Giulio; Kollath, Corinna; Läuchli, Andreas M.
- Physical Review Letters, Vol. 105, Issue 25