η-pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars

Moudgalya, Sanjay; Regnault, Nicolas; Bernevig, B. Andrei

doi:10.1103/physrevb.102.085140

η-pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars

Journal Article · Thu Aug 20 00:00:00 EDT 2020 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.102.085140· OSTI ID:1802875

Moudgalya, Sanjay ^[1]; Regnault, Nicolas ^[2]; Bernevig, B. Andrei ^[3]

Princeton Univ., NJ (United States); OSTI
Princeton Univ., NJ (United States); Ecole Normale Supérieure (ENS), Paris (France); Université PSL, Paris (France); Centre National de la Recherche Scientifique (CNRS), Paris (France); Sorbonne Univ., Paris (France); Université Paris-Diderot (France); Sorbonne Paris Cité (France)
Princeton Univ., NJ (United States)

In this work, we revisit the η-pairing states in Hubbard models and explore their connections to quantum many-body scars to discover a universal scars mechanism. η-pairing occurs due to an algebraic structure known as a spectrum generating algebra (SGA), giving rise to equally spaced towers of eigenstates in the spectrum. We generalize the original η-pairing construction and show that several Hubbard-like models on arbitrary graphs exhibit SGAs, including ones with disorder and spin-orbit coupling. We further define a restricted spectrum generating algebra (RSGA) and give examples of perturbations to the Hubbard-like models that preserve an equally spaced tower of the original model as eigenstates. The states of the surviving tower exhibit a subthermal entanglement entropy, and we analytically obtain parameter regimes for which they lie in the bulk of the spectrum, showing that they are exact quantum many-body scars. The RSGA framework also explains the equally spaced towers of eigenstates in several well-known models of quantum scars, including the Affleck-Kennedy-Lieb-Tasaki model.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: Gordon and Betty Moore Foundation ; National Science Foundation (NSF); Packard Foundation; US Department of the Navy, Office of Naval Research (ONR); USDOE Office of Science (SC); United States-Israel Binational Science Foundation (BSF)

Grant/Contract Number:: SC0016239

OSTI ID:: 1802875

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 8 Vol. 102; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (73)

Extended Hubbard models, eta-pairing and supersymmetry E�ler, Fabian H. L. Journal of Low Temperature Physics, Vol. 99, Issue 3-4 https://doi.org/10.1007/BF00752318	journal	May 1995
Series of hadron energy levels as representations of non-compact groups Dothan, Y.; Gell-Mann, M.; Ne'eman, Y. Physics Letters, Vol. 17, Issue 2 https://doi.org/10.1016/0031-9163(65)90279-9	journal	July 1965
Remarks and generalizations about SU2×SU2 symmetry of Hubbard models Yang, Chen Ning Physics Letters A, Vol. 161, Issue 3 https://doi.org/10.1016/0375-9601(91)90020-9	journal	December 1991
Partial dynamical symmetries Leviatan, A. Progress in Particle and Nuclear Physics, Vol. 66, Issue 1 https://doi.org/10.1016/j.ppnp.2010.08.001	journal	January 2011
The One-Dimensional Hubbard Model Essler, Fabian H. L.; Frahm, Holger; Göhmann, Frank Cambridge University Press https://doi.org/10.1017/CBO9780511534843	book	January 2009
Thermalization and its mechanism for generic isolated quantum systems Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim Nature, Vol. 452, Issue 7189 https://doi.org/10.1038/nature06838	journal	April 2008
Probing many-body dynamics on a 51-atom quantum simulator Bernien, Hannes; Schwartz, Sylvain; Keesling, Alexander Nature, Vol. 551, Issue 7682 https://doi.org/10.1038/nature24622	journal	November 2017
Non-stationary coherent quantum many-body dynamics through dissipation Buča, Berislav; Tindall, Joseph; Jaksch, Dieter Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-09757-y	journal	April 2019
Weak ergodicity breaking from quantum many-body scars Turner, C. J.; Michailidis, A. A.; Abanin, D. A. Nature Physics, Vol. 14, Issue 7 https://doi.org/10.1038/s41567-018-0137-5	journal	May 2018
Quantum scars of bosons with correlated hopping Hudomal, Ana; Vasić, Ivana; Regnault, Nicolas Communications Physics, Vol. 3, Issue 1 https://doi.org/10.1038/s42005-020-0364-9	journal	June 2020
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics D'Alessio, Luca; Kafri, Yariv; Polkovnikov, Anatoli Advances in Physics, Vol. 65, Issue 3 https://doi.org/10.1080/00018732.2016.1198134	journal	May 2016
XXZ model as an effective Hamiltonian for generalized Hubbard models with broken eta -symmetry Albertini, G.; Korepin, V. E.; Schadschneider, A. Journal of Physics A: Mathematical and General, Vol. 28, Issue 10 https://doi.org/10.1088/0305-4470/28/10/004	journal	May 1995
Coherent pairing states for the Hubbard model Solomon, Allan I.; Penson, K. A. Journal of Physics A: Mathematical and General, Vol. 31, Issue 18 https://doi.org/10.1088/0305-4470/31/18/004	journal	May 1998
The Fermion-ladder models: extensions of the Hubbard model with eta-pairing Fan, Heng Journal of Physics A: Mathematical and General, Vol. 32, Issue 48 https://doi.org/10.1088/0305-4470/32/48/101	journal	November 1999
Entanglement and off-diagonal long-range order of an η-pairing state Fan, Heng; Lloyd, Seth Journal of Physics A: Mathematical and General, Vol. 38, Issue 23 https://doi.org/10.1088/0305-4470/38/23/014	journal	May 2005
Connection between quantum-many-body scars and the Affleck–Kennedy–Lieb–Tasaki model from the viewpoint of embedded Hamiltonians Shiraishi, Naoto Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, Issue 8 https://doi.org/10.1088/1742-5468/ab342e	journal	August 2019
Dynamical Groups and Mass Formula Barut, A. O.; Böhm, A. Physical Review, Vol. 139, Issue 4B https://doi.org/10.1103/PhysRev.139.B1107	journal	August 1965
Quantum statistical mechanics in a closed system Deutsch, J. M. Physical Review A, Vol. 43, Issue 4 https://doi.org/10.1103/PhysRevA.43.2046	journal	February 1991
Many-body localization and thermalization in disordered Hubbard chains Mondaini, Rubem; Rigol, Marcos Physical Review A, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevA.92.041601	journal	October 2015
Quantum many-body scars from magnon condensation Iadecola, Thomas; Schecter, Michael; Xu, Shenglong Physical Review B, Vol. 100, Issue 18 https://doi.org/10.1103/PhysRevB.100.184312	journal	November 2019
Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals Iadecola, Thomas; Schecter, Michael Physical Review B, Vol. 101, Issue 2 https://doi.org/10.1103/PhysRevB.101.024306	journal	January 2020
Exact eigenstates in the Lesanovsky model, proximity to integrability and the PXP model, and approximate scar states Mark, Daniel K.; Lin, Cheng-Ju; Motrunich, Olexei I. Physical Review B, Vol. 101, Issue 9 https://doi.org/10.1103/PhysRevB.101.094308	journal	March 2020
Quantum scars as embeddings of weakly broken Lie algebra representations Bull, Kieran; Desaules, Jean-Yves; Papić, Zlatko Physical Review B, Vol. 101, Issue 16 https://doi.org/10.1103/PhysRevB.101.165139	journal	April 2020
Localization from Hilbert space shattering: From theory to physical realizations Khemani, Vedika; Hermele, Michael; Nandkishore, Rahul Physical Review B, Vol. 101, Issue 17 https://doi.org/10.1103/PhysRevB.101.174204	journal	May 2020
Quantum many-body scars from virtual entangled pairs Chattopadhyay, Sambuddha; Pichler, Hannes; Lukin, Mikhail D. Physical Review B, Vol. 101, Issue 17 https://doi.org/10.1103/PhysRevB.101.174308	journal	May 2020
Unified structure for exact towers of scar states in the Affleck-Kennedy-Lieb-Tasaki and other models Mark, Daniel K.; Lin, Cheng-Ju; Motrunich, Olexei I. Physical Review B, Vol. 101, Issue 19 https://doi.org/10.1103/PhysRevB.101.195131	journal	May 2020
Revivals imply quantum many-body scars Alhambra, Álvaro M.; Anshu, Anurag; Wilming, Henrik Physical Review B, Vol. 101, Issue 20 https://doi.org/10.1103/PhysRevB.101.205107	journal	May 2020
Quantum many-body scar states in two-dimensional Rydberg atom arrays Lin, Cheng-Ju; Calvera, Vladimir; Hsieh, Timothy H. Physical Review B, Vol. 101, Issue 22 https://doi.org/10.1103/PhysRevB.101.220304	journal	June 2020
Quantum many-body scars in transverse field Ising ladders and beyond van Voorden, Bart; Minář, Jiří; Schoutens, Kareljan Physical Review B, Vol. 101, Issue 22 https://doi.org/10.1103/PhysRevB.101.220305	journal	June 2020
Exact three-colored quantum scars from geometric frustration Lee, Kyungmin; Melendrez, Ronald; Pal, Arijeet Physical Review B, Vol. 101, Issue 24 https://doi.org/10.1103/PhysRevB.101.241111	journal	June 2020
Collapse and revival of quantum many-body scars via Floquet engineering Mukherjee, Bhaskar; Nandy, Sourav; Sen, Arnab Physical Review B, Vol. 101, Issue 24 https://doi.org/10.1103/PhysRevB.101.245107	journal	June 2020
Large classes of quantum scarred Hamiltonians from matrix product states Moudgalya, Sanjay; O'Brien, Edward; Bernevig, B. Andrei Physical Review B, Vol. 102, Issue 8 https://doi.org/10.1103/PhysRevB.102.085120	journal	August 2020
Superconductivity in an exactly solvable Hubbard model with bond-charge interaction Schadschneider, Andreas Physical Review B, Vol. 51, Issue 16 https://doi.org/10.1103/PhysRevB.51.10386	journal	April 1995
Two generalizations of η pairing in extended Hubbard models Zhai, Hui Physical Review B, Vol. 71, Issue 1 https://doi.org/10.1103/PhysRevB.71.012512	journal	January 2005
Canted spiral: An exact ground state of X X Z zigzag spin ladders Batista, C. D. Physical Review B, Vol. 80, Issue 18 https://doi.org/10.1103/PhysRevB.80.180406	journal	November 2009
η -pairing superfluid in periodically-driven fermionic Hubbard model with strong attraction Kitamura, Sota; Aoki, Hideo Physical Review B, Vol. 94, Issue 17 https://doi.org/10.1103/PhysRevB.94.174503	journal	November 2016
Absence of full many-body localization in the disordered Hubbard chain Prelovšek, P.; Barišić, O. S.; Žnidarič, M. Physical Review B, Vol. 94, Issue 24 https://doi.org/10.1103/PhysRevB.94.241104	journal	December 2016
Counting local integrals of motion in disordered spinless-fermion and Hubbard chains Mierzejewski, Marcin; Kozarzewski, Maciej; Prelovšek, Peter Physical Review B, Vol. 97, Issue 6 https://doi.org/10.1103/PhysRevB.97.064204	journal	February 2018
Beyond many-body localized states in a spin-disordered Hubbard model Yu, Xiongjie; Luo, Di; Clark, Bryan K. Physical Review B, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevB.98.115106	journal	September 2018
Exact ground states for interacting Kitaev chains Wouters, Jurriaan; Katsura, Hosho; Schuricht, Dirk Physical Review B, Vol. 98, Issue 15 https://doi.org/10.1103/PhysRevB.98.155119	journal	October 2018
Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations Turner, C. J.; Michailidis, A. A.; Abanin, D. A. Physical Review B, Vol. 98, Issue 15 https://doi.org/10.1103/PhysRevB.98.155134	journal	October 2018
Exact excited states of nonintegrable models Moudgalya, Sanjay; Rachel, Stephan; Bernevig, B. Andrei Physical Review B, Vol. 98, Issue 23 https://doi.org/10.1103/PhysRevB.98.235155	journal	December 2018
Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis Moudgalya, Sanjay; Regnault, Nicolas; Bernevig, B. Andrei Physical Review B, Vol. 98, Issue 23 https://doi.org/10.1103/PhysRevB.98.235156	journal	December 2018
Signatures of integrability in the dynamics of Rydberg-blockaded chains Khemani, Vedika; Laumann, Chris R.; Chandran, Anushya Physical Review B, Vol. 99, Issue 16 https://doi.org/10.1103/PhysRevB.99.161101	journal	April 2019
Signatures of rare states and thermalization in a theory with confinement Robinson, Neil J.; James, Andrew J. A.; Konik, Robert M. Physical Review B, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevB.99.195108	journal	May 2019
Chaos and quantum thermalization Srednicki, Mark Physical Review E, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevE.50.888	journal	August 1994
Disorder-Induced Localization in a Strongly Correlated Atomic Hubbard Gas Kondov, S. S.; McGehee, W. R.; Xu, W. Physical Review Letters, Vol. 114, Issue 8 https://doi.org/10.1103/PhysRevLett.114.083002	journal	February 2015
Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis Shiraishi, Naoto; Mori, Takashi Physical Review Letters, Vol. 119, Issue 3 https://doi.org/10.1103/PhysRevLett.119.030601	journal	July 2017
Spin Subdiffusion in the Disordered Hubbard Chain Kozarzewski, Maciej; Prelovšek, Peter; Mierzejewski, Marcin Physical Review Letters, Vol. 120, Issue 24 https://doi.org/10.1103/PhysRevLett.120.246602	journal	June 2018
Periodic Orbits, Entanglement, and Quantum Many-Body Scars in Constrained Models: Matrix Product State Approach Ho, Wen Wei; Choi, Soonwon; Pichler, Hannes Physical Review Letters, Vol. 122, Issue 4 https://doi.org/10.1103/PhysRevLett.122.040603	journal	January 2019
Nonthermal States Arising from Confinement in One and Two Dimensions James, Andrew J. A.; Konik, Robert M.; Robinson, Neil J. Physical Review Letters, Vol. 122, Issue 13 https://doi.org/10.1103/PhysRevLett.122.130603	journal	April 2019
Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain Lin, Cheng-Ju; Motrunich, Olexei I. Physical Review Letters, Vol. 122, Issue 17 https://doi.org/10.1103/PhysRevLett.122.173401	journal	April 2019
Emergent SU(2) Dynamics and Perfect Quantum Many-Body Scars Choi, Soonwon; Turner, Christopher J.; Pichler, Hannes Physical Review Letters, Vol. 122, Issue 22 https://doi.org/10.1103/PhysRevLett.122.220603	journal	June 2019
Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models Bull, Kieran; Martin, Ivar; Papić, Z. Physical Review Letters, Vol. 123, Issue 3 https://doi.org/10.1103/PhysRevLett.123.030601	journal	July 2019
Heating-Induced Long-Range η Pairing in the Hubbard Model Tindall, J.; Buča, B.; Coulthard, J. R. Physical Review Letters, Vol. 123, Issue 3 https://doi.org/10.1103/PhysRevLett.123.030603	journal	July 2019
Exact Localized and Ballistic Eigenstates in Disordered Chaotic Spin Ladders and the Fermi-Hubbard Model Iadecola, Thomas; Žnidarič, Marko Physical Review Letters, Vol. 123, Issue 3 https://doi.org/10.1103/PhysRevLett.123.036403	journal	July 2019
Dynamical Scar States in Driven Fracton Systems Pai, Shriya; Pretko, Michael Physical Review Letters, Vol. 123, Issue 13 https://doi.org/10.1103/PhysRevLett.123.136401	journal	September 2019
Weak Ergodicity Breaking and Quantum Many-Body Scars in Spin-1 X Y Magnets Schecter, Michael; Iadecola, Thomas Physical Review Letters, Vol. 123, Issue 14 https://doi.org/10.1103/PhysRevLett.123.147201	journal	October 2019
Quantum Many-Body Scars in Optical Lattices Zhao, Hongzheng; Vovrosh, Joseph; Mintert, Florian Physical Review Letters, Vol. 124, Issue 16 https://doi.org/10.1103/PhysRevLett.124.160604	journal	April 2020
Onsager’s Scars in Disordered Spin Chains Shibata, Naoyuki; Yoshioka, Nobuyuki; Katsura, Hosho Physical Review Letters, Vol. 124, Issue 18 https://doi.org/10.1103/PhysRevLett.124.180604	journal	May 2020
Rigorous results on valence-bond ground states in antiferromagnets Affleck, Ian; Kennedy, Tom; Lieb, Elliott H. Physical Review Letters, Vol. 59, Issue 7 https://doi.org/10.1103/PhysRevLett.59.799	journal	August 1987
η pairing and off-diagonal long-range order in a Hubbard model Yang, Chen Ning Physical Review Letters, Vol. 63, Issue 19 https://doi.org/10.1103/PhysRevLett.63.2144	journal	November 1989
Pseudospin symmetry and new collective modes of the Hubbard model Zhang, Shoucheng Physical Review Letters, Vol. 65, Issue 1 https://doi.org/10.1103/PhysRevLett.65.120	journal	July 1990
Exact demonstration of off-diagonal long-range order in the ground state of a Hubbard model Shen, Shun-Qing; Qiu, Zhao-Ming Physical Review Letters, Vol. 71, Issue 25 https://doi.org/10.1103/PhysRevLett.71.4238	journal	December 1993
η Pairing as a Mechanism of Superconductivity in Models of Strongly Correlated Electrons de Boer, Jan; Korepin, Vladimir E.; Schadschneider, Andreas Physical Review Letters, Vol. 74, Issue 5 https://doi.org/10.1103/PhysRevLett.74.789	journal	January 1995
Topological many-body scar states in dimensions one, two, and three Ok, Seulgi; Choo, Kenny; Mudry, Christopher Physical Review Research, Vol. 1, Issue 3 https://doi.org/10.1103/PhysRevResearch.1.033144	journal	December 2019
Stabilizing two-dimensional quantum scars by deformation and synchronization Michailidis, A. A.; Turner, C. J.; Papić, Z. Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.022065	journal	June 2020
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians Sala, Pablo; Rakovszky, Tibor; Verresen, Ruben Physical Review X, Vol. 10, Issue 1 https://doi.org/10.1103/PhysRevX.10.011047	journal	February 2020
Slow Quantum Thermalization and Many-Body Revivals from Mixed Phase Space Michailidis, A. A.; Turner, C. J.; Papić, Z. Physical Review X, Vol. 10, Issue 1 https://doi.org/10.1103/PhysRevX.10.011055	journal	March 2020
Lattice Gauge Theories and String Dynamics in Rydberg Atom Quantum Simulators Surace, Federica M.; Mazza, Paolo P.; Giudici, Giuliano Physical Review X, Vol. 10, Issue 2 https://doi.org/10.1103/PhysRevX.10.021041	journal	May 2020
SO ₄ SYMMETRY IN A HUBBARD MODEL Yang, Chen Ning; Zhang, S. C. Modern Physics Letters B, Vol. 04, Issue 11 https://doi.org/10.1142/S0217984990000933	journal	June 1990
Many-Body Localization and Thermalization in Quantum Statistical Mechanics Nandkishore, Rahul; Huse, David A. Annual Review of Condensed Matter Physics, Vol. 6, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031214-014726	journal	March 2015
Entanglement of exact excited eigenstates of the Hubbard model in arbitrary dimension Vafek, Oskar; Regnault, Nicolas; Bernevig, B. Andrei SciPost Physics, Vol. 3, Issue 6 https://doi.org/10.21468/SciPostPhys.3.6.043	journal	January 2017

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