Superdiffusion from Emergent Classical Solitons in Quantum Spin Chains

De Nardis, Jacopo; Gopalakrishnan, Sarang; Ilievski, Enej; Vasseur, Romain

doi:10.1103/physrevlett.125.070601

Superdiffusion from Emergent Classical Solitons in Quantum Spin Chains

Journal Article · Wed Aug 12 00:00:00 EDT 2020 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.125.070601· OSTI ID:1647653

De Nardis, Jacopo ^[1]; Gopalakrishnan, Sarang ^[2]; Ilievski, Enej ^[3]; Vasseur, Romain ^[4]

Univ. of Ghent (Belgium); UMass Amherst
CUNY College of Staten Island, Staten Island, NY (United States); CUNY, NY (United States)
Univ. of Ljubljana (Slovenia)
Univ. of Massachusetts, Amherst, MA (United States)

Finite-temperature spin transport in the quantum Heisenberg spin chain is known to be superdiffusive, and has been conjectured to lie in the Kardar-Parisi-Zhang (KPZ) universality class. Using a kinetic theory of transport, we compute the KPZ coupling strength for the Heisenberg chain as a function of temperature, directly from microscopics; the results agree well with density-matrix renormalization group simulations. Here, we establish a rigorous quantum-classical correspondence between the “giant quasiparticles” that govern superdiffusion and solitons in the classical continuous Landau-Lifshitz ferromagnet. We conclude that KPZ universality has the same origin in classical and quantum integrable isotropic magnets: a finite-temperature gas of low-energy classical solitons.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; NSF

Grant/Contract Number:: SC0019168

OSTI ID:: 1647653

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 7 Vol. 125; ISSN 1079-7114; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (96)

Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with ultracold atoms Schneider, Ulrich; Hackermüller, Lucia; Ronzheimer, Jens Philipp Nature Physics, Vol. 8, Issue 3 https://doi.org/10.1038/nphys2205	journal	January 2012
Solitons in the statistical mechanics of the Toda lattice Bolterauer, H.; Opper, M. Zeitschrift f�r Physik B Condensed Matter, Vol. 42, Issue 2 https://doi.org/10.1007/BF01319550	journal	June 1981
Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem Horváth, D. X. Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/JHEP10(2019)020	journal	October 2019
Finite Time Corrections in KPZ Growth Models Ferrari, Patrik L.; Frings, René Journal of Statistical Physics, Vol. 144, Issue 6 https://doi.org/10.1007/s10955-011-0318-4	journal	September 2011
Nonlinear Fluctuating Hydrodynamics for Anharmonic Chains Spohn, Herbert Journal of Statistical Physics, Vol. 154, Issue 5 https://doi.org/10.1007/s10955-014-0933-y	journal	February 2014
The One-Dimensional KPZ Equation and Its Universality Class Quastel, Jeremy; Spohn, Herbert Journal of Statistical Physics, Vol. 160, Issue 4 https://doi.org/10.1007/s10955-015-1250-9	journal	April 2015
Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain Das, Avijit; Damle, Kedar; Dhar, Abhishek Journal of Statistical Physics https://doi.org/10.1007/s10955-019-02397-y	journal	October 2019
Review of AdS/CFT Integrability: An Overview Beisert, Niklas; Ahn, Changrim; Alday, Luis F. Letters in Mathematical Physics, Vol. 99, Issue 1-3 https://doi.org/10.1007/s11005-011-0529-2	journal	October 2011
Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models Zamolodchikov, Alexander B.; Zamolodchikov, Alexey B. Annals of Physics, Vol. 120, Issue 2 https://doi.org/10.1016/0003-4916(79)90391-9	journal	August 1979
Integration of the continuous Heisenberg spin chain through the inverse scattering method Takhtajan, L. A. Physics Letters A, Vol. 64, Issue 2 https://doi.org/10.1016/0375-9601(77)90727-7	journal	December 1977
The soliton-gas analogy for the Toda lattice Mertens, F. G.; Büttner, H. Physics Letters A, Vol. 84, Issue 6 https://doi.org/10.1016/0375-9601(81)90776-3	journal	August 1981
Classical thermodynamics of the Heisenberg chain in a field by generalized Bethe ansatz method Bullough, R. K.; Chen, Y. -z.; Timonen, J. Physics Letters A, Vol. 145, Issue 4 https://doi.org/10.1016/0375-9601(90)90671-A	journal	April 1990
On the dynamics of a continuum spin system Lakshmanan, M.; Ruijgrok, Th. W.; Thompson, C. J. Physica A: Statistical Mechanics and its Applications, Vol. 84, Issue 3 https://doi.org/10.1016/0378-4371(76)90106-0	journal	January 1976
Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states Basko, D. M.; Aleiner, I. L.; Altshuler, B. L. Annals of Physics, Vol. 321, Issue 5 https://doi.org/10.1016/j.aop.2005.11.014	journal	May 2006
Finite-size effects from giant magnons Arutyunov, Gleb; Frolov, Sergey; Zamaklar, Marija Nuclear Physics B, Vol. 778, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2006.12.026	journal	August 2007
Finite size effects for giant magnons on physical strings Minahan, J. A.; Ohlsson Sax, O. Nuclear Physics B, Vol. 801, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2008.04.018	journal	September 2008
Heat transport of cuprate-based low-dimensional quantum magnets with strong exchange coupling Hess, Christian Physics Reports, Vol. 811 https://doi.org/10.1016/j.physrep.2019.02.004	journal	June 2019
Exact Scaling Functions for One-Dimensional Stationary KPZ Growth Prähofer, Michael; Spohn, Herbert Journal of Statistical Physics, Vol. 115, Issue 1/2 https://doi.org/10.1023/B:JOSS.0000019810.21828.fc	journal	April 2004
A quantum Newton's cradle Kinoshita, Toshiya; Wenger, Trevor; Weiss, David S. Nature, Vol. 440, Issue 7086 https://doi.org/10.1038/nature04693	journal	April 2006
Non-equilibrium coherence dynamics in one-dimensional Bose gases Hofferberth, S.; Lesanovsky, I.; Fischer, B. Nature, Vol. 449, Issue 7160 https://doi.org/10.1038/nature06149	journal	September 2007
Observation of quantized conductance in neutral matter Krinner, Sebastian; Stadler, David; Husmann, Dominik Nature, Vol. 517, Issue 7532 https://doi.org/10.1038/nature14049	journal	December 2014
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
Spin diffusion from an inhomogeneous quench in an integrable system Ljubotina, Marko; Žnidarič, Marko; Prosen, Tomaž Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms16117	journal	July 2017
Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain Mourigal, Martin; Enderle, Mechthild; Klöpperpieper, Axel Nature Physics, Vol. 9, Issue 7 https://doi.org/10.1038/nphys2652	journal	June 2013
Universal dynamics in an isolated one-dimensional Bose gas far from equilibrium Erne, Sebastian; Bücker, Robert; Gasenzer, Thomas Nature, Vol. 563, Issue 7730 https://doi.org/10.1038/s41586-018-0667-0	journal	November 2018
Growing interfaces uncover universal fluctuations behind scale invariance Takeuchi, Kazumasa A.; Sano, Masaki; Sasamoto, Tomohiro Scientific Reports, Vol. 1, Issue 1 https://doi.org/10.1038/srep00034	journal	July 2011
Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction Yang, C. N.; Yang, C. P. Journal of Mathematical Physics, Vol. 10, Issue 7 https://doi.org/10.1063/1.1664947	journal	July 1969
Anomalous relaxation and the high-temperature structure factor of XXZ spin chains Gopalakrishnan, Sarang; Vasseur, Romain; Ware, Brayden Proceedings of the National Academy of Sciences, Vol. 116, Issue 33 https://doi.org/10.1073/pnas.1906914116	journal	July 2019
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
The Bethe-ansatz for Script N = 4 super Yang-Mills Minahan, Joseph A.; Zarembo, Konstantin Journal of High Energy Physics, Vol. 2003, Issue 03 https://doi.org/10.1088/1126-6708/2003/03/013	journal	March 2003
Classical/quantum integrability in AdS/CFT A. Kazakov, V.; Marshakov, A.; A. Minahan, J. Journal of High Energy Physics, Vol. 2004, Issue 05 https://doi.org/10.1088/1126-6708/2004/05/024	journal	May 2004
Magnon bound-state scattering in gauge and string theory Roiban, Radu Journal of High Energy Physics, Vol. 2007, Issue 04 https://doi.org/10.1088/1126-6708/2007/04/048	journal	April 2007
Quantum stability for the Heisenberg ferromagnet Bargheer, Till; Beisert, Niklas; Gromov, Nikolay New Journal of Physics, Vol. 10, Issue 10 https://doi.org/10.1088/1367-2630/10/10/103023	journal	October 2008
Low temperature dynamics of nonlinear Luttinger liquids Karrasch, C.; Pereira, R. G.; Sirker, J. New Journal of Physics, Vol. 17, Issue 10 https://doi.org/10.1088/1367-2630/17/10/103003	journal	September 2015
Nonequilibrium quantum dynamics and transport: from integrability to many-body localization Vasseur, Romain; Moore, Joel E. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6 https://doi.org/10.1088/1742-5468/2016/06/064010	journal	June 2016
Equilibration properties of classical integrable field theories De Luca, Andrea; Mussardo, Giuseppe Journal of Statistical Mechanics: Theory and Experiment, Vol. 2016, Issue 6 https://doi.org/10.1088/1742-5468/2016/06/064011	journal	June 2016
Dynamics of hard rods with initial domain wall state Doyon, Benjamin; Spohn, Herbert Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 7 https://doi.org/10.1088/1742-5468/aa7abf	journal	July 2017
A TBA approach to thermal transport in the XXZ Heisenberg model Zotos, X. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2017, Issue 10 https://doi.org/10.1088/1742-5468/aa8c13	journal	October 2017
Hydrodynamic long-time tails after a quantum quench Lux, Jonathan; Müller, Jan; Mitra, Aditi Physical Review A, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevA.89.053608	journal	May 2014
Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics Bertini, Bruno; Piroli, Lorenzo; Kormos, Márton Physical Review B, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevB.100.035108	journal	July 2019
Kardar-Parisi-Zhang universality from soft gauge modes Bulchandani, Vir B. Physical Review B, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevB.101.041411	journal	January 2020
Universal spin dynamics in infinite-temperature one-dimensional quantum magnets Dupont, Maxime; Moore, Joel E. Physical Review B, Vol. 101, Issue 12 https://doi.org/10.1103/PhysRevB.101.121106	journal	March 2020
Diffusive hydrodynamics from integrability breaking Friedman, Aaron J.; Gopalakrishnan, Sarang; Vasseur, Romain Physical Review B, Vol. 101, Issue 18 https://doi.org/10.1103/PhysRevB.101.180302	journal	May 2020
Soliton-breather approach to classical sine-Gordon thermodynamics Sasaki, Kazuo Physical Review B, Vol. 33, Issue 4 https://doi.org/10.1103/PhysRevB.33.2214	journal	February 1986
Exact Bethe-ansatz thermodynamics for the sine-Gordon model in the classical limit: Effect of long strings Timonen, J.; Bullough, R. K.; Pilling, D. J. Physical Review B, Vol. 34, Issue 9 https://doi.org/10.1103/PhysRevB.34.6525	journal	November 1986
Nontopological thermal solitons in isotropic ferromagnetic lattices Theodorakopoulos, N. Physical Review B, Vol. 52, Issue 13 https://doi.org/10.1103/PhysRevB.52.9507	journal	October 1995
Haldane-gapped spin chains as Luttinger liquids: Correlation functions at finite field Konik, Robert M.; Fendley, Paul Physical Review B, Vol. 66, Issue 14 https://doi.org/10.1103/PhysRevB.66.144416	journal	October 2002
Ballistic transport in the one-dimensional Hubbard model: The hydrodynamic approach Ilievski, Enej; De Nardis, Jacopo Physical Review B, Vol. 96, Issue 8 https://doi.org/10.1103/PhysRevB.96.081118	journal	August 2017
Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph Physical Review B, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevB.97.045407	journal	January 2018
Analytic solution of the domain-wall nonequilibrium stationary state Collura, Mario; De Luca, Andrea; Viti, Jacopo Physical Review B, Vol. 97, Issue 8 https://doi.org/10.1103/PhysRevB.97.081111	journal	February 2018
Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems Gopalakrishnan, Sarang; Huse, David A.; Khemani, Vedika Physical Review B, Vol. 98, Issue 22 https://doi.org/10.1103/PhysRevB.98.220303	journal	December 2018
Domain-wall dynamics in the Landau-Lifshitz magnet and the classical-quantum correspondence for spin transport Gamayun, Oleksandr; Miao, Yuan; Ilievski, Enej Physical Review B, Vol. 99, Issue 14 https://doi.org/10.1103/PhysRevB.99.140301	journal	April 2019
Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains Agrawal, Utkarsh; Gopalakrishnan, Sarang; Vasseur, Romain Physical Review B, Vol. 99, Issue 17 https://doi.org/10.1103/PhysRevB.99.174203	journal	May 2019
Semiclassical scattering of quantized nonlinear waves Jackiw, R.; Woo, G. Physical Review D, Vol. 12, Issue 6 https://doi.org/10.1103/PhysRevD.12.1643	journal	September 1975
Kardar-Parisi-Zhang scaling for an integrable lattice Landau-Lifshitz spin chain Das, Avijit; Kulkarni, Manas; Spohn, Herbert Physical Review E, Vol. 100, Issue 4 https://doi.org/10.1103/PhysRevE.100.042116	journal	October 2019
Spin Transport in a One-Dimensional Anisotropic Heisenberg Model Žnidarič, Marko Physical Review Letters, Vol. 106, Issue 22 https://doi.org/10.1103/PhysRevLett.106.220601	journal	May 2011
Finite-Temperature Dynamical Density Matrix Renormalization Group and the Drude Weight of Spin- 1 / 2 Chains Karrasch, C.; Bardarson, J. H.; Moore, J. E. Physical Review Letters, Vol. 108, Issue 22 https://doi.org/10.1103/PhysRevLett.108.227206	journal	May 2012
Far-from-Equilibrium Spin Transport in Heisenberg Quantum Magnets Hild, Sebastian; Fukuhara, Takeshi; Schauß, Peter Physical Review Letters, Vol. 113, Issue 14 https://doi.org/10.1103/PhysRevLett.113.147205	journal	October 2014
Absence of Diffusion in an Interacting System of Spinless Fermions on a One-Dimensional Disordered Lattice Bar Lev, Yevgeny; Cohen, Guy; Reichman, David R. Physical Review Letters, Vol. 114, Issue 10 https://doi.org/10.1103/PhysRevLett.114.100601	journal	March 2015
Anomalous Diffusion and Griffiths Effects Near the Many-Body Localization Transition Agarwal, Kartiek; Gopalakrishnan, Sarang; Knap, Michael Physical Review Letters, Vol. 114, Issue 16 https://doi.org/10.1103/PhysRevLett.114.160401	journal	April 2015
Transport in Out-of-Equilibrium X X Z Chains: Exact Profiles of Charges and Currents Bertini, Bruno; Collura, Mario; De Nardis, Jacopo Physical Review Letters, Vol. 117, Issue 20 https://doi.org/10.1103/PhysRevLett.117.207201	journal	November 2016
Microscopic Origin of Ideal Conductivity in Integrable Quantum Models Ilievski, Enej; De Nardis, Jacopo Physical Review Letters, Vol. 119, Issue 2 https://doi.org/10.1103/PhysRevLett.119.020602	journal	July 2017
Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics Doyon, Benjamin; Dubail, Jérôme; Konik, Robert Physical Review Letters, Vol. 119, Issue 19 https://doi.org/10.1103/PhysRevLett.119.195301	journal	November 2017
Solvable Hydrodynamics of Quantum Integrable Systems Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph Physical Review Letters, Vol. 119, Issue 22 https://doi.org/10.1103/PhysRevLett.119.220604	journal	November 2017
Soliton Gases and Generalized Hydrodynamics Doyon, Benjamin; Yoshimura, Takato; Caux, Jean-Sébastien Physical Review Letters, Vol. 120, Issue 4 https://doi.org/10.1103/PhysRevLett.120.045301	journal	January 2018
Incomplete Thermalization from Trap-Induced Integrability Breaking: Lessons from Classical Hard Rods Cao, Xiangyu; Bulchandani, Vir B.; Moore, Joel E. Physical Review Letters, Vol. 120, Issue 16 https://doi.org/10.1103/PhysRevLett.120.164101	journal	April 2018
Nonequilibrium Mass Transport in the 1D Fermi-Hubbard Model Scherg, S.; Kohlert, T.; Herbrych, J. Physical Review Letters, Vol. 121, Issue 13 https://doi.org/10.1103/PhysRevLett.121.130402	journal	September 2018
Hydrodynamic Diffusion in Integrable Systems De Nardis, Jacopo; Bernard, Denis; Doyon, Benjamin Physical Review Letters, Vol. 121, Issue 16 https://doi.org/10.1103/PhysRevLett.121.160603	journal	October 2018
Superdiffusion in One-Dimensional Quantum Lattice Models Ilievski, Enej; De Nardis, Jacopo; Medenjak, Marko Physical Review Letters, Vol. 121, Issue 23 https://doi.org/10.1103/PhysRevLett.121.230602	journal	December 2018
Kinetic Theory of Spin Diffusion and Superdiffusion in X X Z Spin Chains Gopalakrishnan, Sarang; Vasseur, Romain Physical Review Letters, Vol. 122, Issue 12 https://doi.org/10.1103/PhysRevLett.122.127202	journal	March 2019
Kardar-Parisi-Zhang Physics in the Quantum Heisenberg Magnet Ljubotina, Marko; Žnidarič, Marko; Prosen, Tomaž Physical Review Letters, Vol. 122, Issue 21 https://doi.org/10.1103/PhysRevLett.122.210602	journal	May 2019
Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions Bastianello, Alvise; Alba, Vincenzo; Caux, Jean-Sébastien Physical Review Letters, Vol. 123, Issue 13 https://doi.org/10.1103/PhysRevLett.123.130602	journal	September 2019
Anomalous Spin Diffusion in One-Dimensional Antiferromagnets De Nardis, Jacopo; Medenjak, Marko; Karrasch, Christoph Physical Review Letters, Vol. 123, Issue 18 https://doi.org/10.1103/PhysRevLett.123.186601	journal	October 2019
Quantum Generalized Hydrodynamics Ruggiero, Paola; Calabrese, Pasquale; Doyon, Benjamin Physical Review Letters, Vol. 124, Issue 14 https://doi.org/10.1103/PhysRevLett.124.140603	journal	April 2020
Dynamic Scaling of Growing Interfaces Kardar, Mehran; Parisi, Giorgio; Zhang, Yi-Cheng Physical Review Letters, Vol. 56, Issue 9 https://doi.org/10.1103/PhysRevLett.56.889	journal	March 1986
Semiclassical solitons and the S =1/2 Heisenberg model Theodorakopoulos, N.; Bacalis, N. C. Physical Review Letters, Vol. 67, Issue 21 https://doi.org/10.1103/PhysRevLett.67.3018	journal	November 1991
Low-Lying Eigenstates of the One-Dimensional Heisenberg Ferromagnet for any Magnetization and Momentum Sutherland, Bill Physical Review Letters, Vol. 74, Issue 5 https://doi.org/10.1103/PhysRevLett.74.816	journal	January 1995
Bloch Walls and Macroscopic String States in Bethe's Solution of the Heisenberg Ferromagnetic Linear Chain Dhar, Abhishek; Sriram Shastry, B. Physical Review Letters, Vol. 85, Issue 13 https://doi.org/10.1103/PhysRevLett.85.2813	journal	September 2000
Current Operators in Bethe Ansatz and Generalized Hydrodynamics: An Exact Quantum-Classical Correspondence Borsi, Márton; Pozsgay, Balázs; Pristyák, Levente Physical Review X, Vol. 10, Issue 1 https://doi.org/10.1103/PhysRevX.10.011054	journal	March 2020
Emergent Hydrodynamics in Integrable Quantum Systems Out of Equilibrium Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Yoshimura, Takato Physical Review X, Vol. 6, Issue 4 https://doi.org/10.1103/PhysRevX.6.041065	journal	December 2016
Quantum Entanglement Growth under Random Unitary Dynamics Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevX.7.031016	journal	July 2017
Thermalization near Integrability in a Dipolar Quantum Newton’s Cradle Tang, Yijun; Kao, Wil; Li, Kuan-Yu Physical Review X, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevX.8.021030	journal	May 2018
Colloquium : Nonequilibrium dynamics of closed interacting quantum systems Polkovnikov, Anatoli; Sengupta, Krishnendu; Silva, Alessandro Reviews of Modern Physics, Vol. 83, Issue 3 https://doi.org/10.1103/RevModPhys.83.863	journal	August 2011
Colloquium : Many-body localization, thermalization, and entanglement Abanin, Dmitry A.; Altman, Ehud; Bloch, Immanuel Reviews of Modern Physics, Vol. 91, Issue 2 https://doi.org/10.1103/RevModPhys.91.021001	journal	May 2019
Relaxation and Prethermalization in an Isolated Quantum System Gring, M.; Kuhnert, M.; Langen, T. Science, Vol. 337, Issue 6100 https://doi.org/10.1126/science.1224953	journal	September 2012
Observation of many-body localization of interacting fermions in a quasirandom optical lattice Schreiber, M.; Hodgman, S. S.; Bordia, P. Science, Vol. 349, Issue 6250 https://doi.org/10.1126/science.aaa7432	journal	July 2015
Spin transport in a Mott insulator of ultracold fermions Nichols, Matthew A.; Cheuk, Lawrence W.; Okan, Melih Science, Vol. 363, Issue 6425 https://doi.org/10.1126/science.aat4387	journal	December 2018
Observation of dynamical fermionization Wilson, Joshua M.; Malvania, Neel; Le, Yuan Science, Vol. 367, Issue 6485 https://doi.org/10.1126/science.aaz0242	journal	March 2020
One-Dimensional Heisenberg Model at Finite Temperature Takahashi, Minoru Progress of Theoretical Physics, Vol. 46, Issue 2 https://doi.org/10.1143/PTP.46.401	journal	August 1971
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
A note on generalized hydrodynamics: inhomogeneous fields and other concepts Doyon, Benjamin; Yoshimura, Takato SciPost Physics, Vol. 2, Issue 2 https://doi.org/10.21468/SciPostPhys.2.2.014	journal	January 2017
Drude Weight for the Lieb-Liniger Bose Gas Doyon, Benjamin; Spohn, Herbert SciPost Physics, Vol. 3, Issue 6 https://doi.org/10.21468/SciPostPhys.3.6.039	journal	January 2017
Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model Bastianello, Alvise; Doyon, Benjamin; Watts, Gerard SciPost Physics, Vol. 4, Issue 6 https://doi.org/10.21468/SciPostPhys.4.6.045	journal	January 2018
Diffusion in generalized hydrodynamics and quasiparticle scattering De Nardis, Jacopo; Bernard, Denis; Doyon, Benjamin SciPost Physics, Vol. 6, Issue 4 https://doi.org/10.21468/SciPostPhys.6.4.049	journal	January 2019
Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point Misguich, Grégoire; Pavloff, Nicolas; Pasquier, Vincent SciPost Physics, Vol. 7, Issue 2 https://doi.org/10.21468/SciPostPhys.7.2.025	journal	January 2019
Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models Møller, Frederik Skovbo; Schmiedmayer, Jörg SciPost Physics, Vol. 8, Issue 3 https://doi.org/10.21468/SciPostPhys.8.3.041	journal	January 2020

Cited By (5)

Algebraic Construction of Current Operators in Integrable Spin Chains Pozsgay, Balázs Physical Review Letters, Vol. 125, Issue 7 https://doi.org/10.1103/physrevlett.125.070602	journal	August 2020
Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain Miao, Yuan; Ilievski, Enej; Gamayun, Oleksandr SciPost Physics, Vol. 10, Issue 4 https://doi.org/10.21468/scipostphys.10.4.086	journal	April 2021
Hydrodynamics of nonintegrable systems from a relaxation-time approximation Lopez-Piqueres, Javier; Ware, Brayden; Gopalakrishnan, Sarang arXiv https://doi.org/10.48550/arxiv.2005.13546	text	January 2020
Weak integrability breaking: chaos with integrability signature in coherent diffusion Znidaric, Marko arXiv https://doi.org/10.48550/arxiv.2006.09793	text	January 2020
Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss Hutsalyuk, Arthur; Pozsgay, Balázs arXiv https://doi.org/10.48550/arxiv.2012.15640	text	January 2020

Similar Records

Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

Journal Article · Fri Apr 05 00:00:00 EDT 2024 · Science · OSTI ID:2579986

Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems

Journal Article · Mon Nov 20 23:00:00 EST 2023 · Annual Review of Condensed Matter Physics · OSTI ID:2376128

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

Journal Article · Thu Sep 10 00:00:00 EDT 2020 · Physical Review. B · OSTI ID:1663368

Related Subjects

1-dimensional spin chains
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Kardar-Parisi-Zhang equation
Solitons
Transport phenomena

Superdiffusion from Emergent Classical Solitons in Quantum Spin Chains

Citation Formats

References (96)

Cited By (5)

Similar Records

Related Subjects