Integrable Many-Body Quantum Floquet-Thouless Pumps

Friedman, Aaron J.; Gopalakrishnan, Sarang; Vasseur, Romain

doi:10.1103/PhysRevLett.123.170603

Title: Integrable Many-Body Quantum Floquet-Thouless Pumps

Journal Article · 23 October 2019 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.123.170603 · OSTI ID:1593349

Friedman, Aaron J. ^[1]; Gopalakrishnan, Sarang ^[2]; Vasseur, Romain ^[3]

Univ. of California, Irvine, CA (United States). Dept. of Physics and Astronomy; Univ. of Massachusetts, Amherst, MA (United States). Dept. of Physics; UMass Amherst
City Univ. of New York (CUNY), NY (United States)
Univ. of Massachusetts, Amherst, MA (United States). Dept. of Physics

We construct an interacting integrable Floquet model featuring quasiparticle excitations with topologically nontrivial chiral dispersion. This model is a fully quantum generalization of an integrable classical cellular automaton. Here, we write down and solve the Bethe equations for the generalized quantum model and show that these take on a particularly simple form that allows for an exact solution: essentially, the quasiparticles behave like interacting hard rods. The generalized thermodynamics and hydrodynamics of this model follow directly, providing an exact description of interacting chiral particles in the thermodynamic limit. Although the model is interacting, its unusually simple structure allows us to construct operators that spread with no butterfly effect; this construction does not seem possible in other interacting integrable systems. This model exemplifies a new class of exactly solvable, interacting quantum systems specific to the Floquet setting.

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Research Organization:: Univ. of Massachusetts, Amherst, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)

Grant/Contract Number:: SC0019168

OSTI ID:: 1593349

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 17 Vol. 123; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Area laws in a many-body localized state and its implications for topological order Bauer, Bela; Nayak, Chetan arXiv https://doi.org/10.48550/arxiv.1306.5753	text	January 2013
Localization and topology protected quantum coherence at the edge of 'hot' matter Bahri, Yasaman; Vosk, Ronen; Altman, Ehud arXiv https://doi.org/10.48550/arxiv.1307.4092	preprint	January 2013
Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices Aidelsburger, M.; Atala, M.; Lohse, M. arXiv https://doi.org/10.48550/arxiv.1308.0321	text	January 2013
Equilibrium states of generic quantum systems subject to periodic driving Lazarides, Achilleas; Das, Arnab; Moessner, Roderich arXiv https://doi.org/10.48550/arxiv.1403.2946	text	January 2014
Many body localization and thermalization in quantum statistical mechanics Nandkishore, Rahul; Huse, David A. arXiv https://doi.org/10.48550/arxiv.1404.0686	text	January 2014
Far-from-equilibrium spin transport in Heisenberg quantum magnets Hild, Sebastian; Fukuhara, Takeshi; Schauß, Peter arXiv https://doi.org/10.48550/arxiv.1407.6934	text	January 2014
Fate of many-body localization under periodic driving Lazarides, Achilleas; Das, Arnab; Moessner, Roderich arXiv https://doi.org/10.48550/arxiv.1410.3455	text	January 2014
A bound on chaos Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas arXiv https://doi.org/10.48550/arxiv.1503.01409	text	January 2015
Exponentially slow heating in periodically driven many-body systems Abanin, Dmitry; De Roeck, Wojciech; Huveneers, François arXiv https://doi.org/10.48550/arxiv.1507.01474	text	January 2015
Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms Meinert, Florian; Mark, Manfred J.; Lauber, Katharina arXiv https://doi.org/10.48550/arxiv.1602.02657	text	January 2016
Classification of topological phases in periodically driven interacting systems Else, Dominic V.; Nayak, Chetan arXiv https://doi.org/10.48550/arxiv.1602.04804	text	January 2016
Universal chiral quasi-steady states in periodically driven many-body systems Lindner, Netanel H.; Berg, Erez; Rudner, Mark S. arXiv https://doi.org/10.48550/arxiv.1603.03053	text	January 2016
Nonequilibrium quantum dynamics and transport: from integrability to many-body localization Vasseur, Romain; Moore, Joel E. arXiv https://doi.org/10.48550/arxiv.1603.06618	text	January 2016
Generalized Gibbs ensemble in integrable lattice models Vidmar, Lev; Rigol, Marcos arXiv https://doi.org/10.48550/arxiv.1604.03990	text	January 2016
Emergent hydrodynamics in integrable quantum systems out of equilibrium Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Yoshimura, Takato arXiv https://doi.org/10.48550/arxiv.1605.07331	text	January 2016
Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents Bertini, Bruno; Collura, Mario; De Nardis, Jacopo arXiv https://doi.org/10.48550/arxiv.1605.09790	text	January 2016
Pre-thermal phases of matter protected by time-translation symmetry Else, Dominic V.; Bauer, Bela; Nayak, Chetan arXiv https://doi.org/10.48550/arxiv.1607.05277	text	January 2016
Discrete time crystals: rigidity, criticality, and realizations Yao, Norman Y.; Potter, Andrew C.; Potirniche, Ionut-Dragos arXiv https://doi.org/10.48550/arxiv.1608.02589	text	January 2016
Observation of a Discrete Time Crystal Zhang, J.; Hess, P. W.; Kyprianidis, A. arXiv https://doi.org/10.48550/arxiv.1609.08684	text	January 2016
Floquet topological phases with symmetry in all dimensions Roy, Rahul; Harper, Fenner arXiv https://doi.org/10.48550/arxiv.1610.06899	text	January 2016
A note on generalized hydrodynamics: inhomogeneous fields and other concepts Doyon, Benjamin; Yoshimura, Takato arXiv https://doi.org/10.48550/arxiv.1611.08225	text	January 2016
Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains De Luca, Andrea; Collura, Mario; De Nardis, Jacopo arXiv https://doi.org/10.48550/arxiv.1612.07265	text	January 2016
Microscopic origin of ideal conductivity in integrable quantum models Ilievski, Enej; De Nardis, Jacopo arXiv https://doi.org/10.48550/arxiv.1702.02930	text	January 2017
Critical Time Crystals in Dipolar Systems Ho, Wen Wei; Choi, Soonwon; Lukin, Mikhail D. arXiv https://doi.org/10.48550/arxiv.1703.04593	text	January 2017
Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach Ilievski, Enej; De Nardis, Jacopo arXiv https://doi.org/10.48550/arxiv.1706.05931	text	January 2017
On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems Bulchandani, Vir B. arXiv https://doi.org/10.48550/arxiv.1706.06278	text	January 2017
Analytic solution of the Domain Wall non-equilibrium stationary state Collura, Mario; De Luca, Andrea; Viti, Jacopo arXiv https://doi.org/10.48550/arxiv.1707.06218	text	January 2017
Incomplete thermalization from trap-induced integrability breaking: lessons from classical hard rods Cao, Xiangyu; Bulchandani, Vir B.; Moore, Joel E. arXiv https://doi.org/10.48550/arxiv.1710.09330	text	January 2017
Topological Floquet-Thouless energy pump Kolodrubetz, Michael H.; Nathan, Frederik; Gazit, Snir arXiv https://doi.org/10.48550/arxiv.1711.00014	text	January 2017
Low-Temperature Transport in Out-of-Equilibrium XXZ Chains Bertini, Bruno; Piroli, Lorenzo arXiv https://doi.org/10.48550/arxiv.1711.00519	text	January 2017
Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup Caux, Jean-Sébastien; Doyon, Benjamin; Dubail, Jérôme arXiv https://doi.org/10.48550/arxiv.1711.00873	text	January 2017
Quantum Computing in the NISQ era and beyond Preskill, John arXiv https://doi.org/10.48550/arxiv.1801.00862	text	January 2018
Operator growth and eigenstate entanglement in an interacting integrable Floquet system Gopalakrishnan, Sarang arXiv https://doi.org/10.48550/arxiv.1806.04156	text	January 2018
Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain Alba, Vincenzo; Dubail, Jerome; Medenjak, Marko arXiv https://doi.org/10.48550/arxiv.1901.04521	text	January 2019
Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states Basko, D. M.; Aleiner, I. L.; Altshuler, B. L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0506617	text	January 2005
Localization of interacting fermions at high temperature Oganesyan, Vadim; Huse, David A. arXiv https://doi.org/10.48550/arxiv.cond-mat/0610854	text	January 2006
Time evolution of a quantum many-body system: transition from integrability to ergodicity in thermodynamic limit Prosen, Tomaz arXiv https://doi.org/10.48550/arxiv.cond-mat/9707180	text	January 1997
Ergodic properties of a generic non-integrable quantum many-body system in thermodynamic limit Prosen, Tomaz arXiv https://doi.org/10.48550/arxiv.cond-mat/9808150	text	January 1998

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