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This review summarizes recent advances in our understanding of anomalous transport in spin chains, viewed through the lens of integrability.
B. Doyon, “Diffusion and superdiffusion from hydrodynamic projection,” (2019), arXiv:1912.01551
1912
Earlier work this paper cites.
R. Kubo, “Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems,” Journal of the Physical Society of Japan 12
1957
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R. Kubo, M. Yokota, and S. Nakajima, “Statistical-Mechanical Theory of Irreversible Processes. II. Response to Thermal Disturbance,” Journal of the Physical Society of Japan 12
1957
Earlier work this paper cites.
W. Kohn, “Theory of the insulating state,” Physical Review 133
1964
Earlier work this paper cites.
J. M. Luttinger, “Theory of thermal transport coefficients,” Phys. Rev. 135
1964
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C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, “Method for Solving the Korteweg-deVries Equation,” Phys. Rev. Lett. 19
1967
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P. D. Lax, “Integrals of nonlinear equations of evolution and solitary waves,” Communications on Pure and Applied Mathematics 21
1968
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P. Mazur, “Non-ergodicity of phase functions in certain systems,” Physica 43
1969
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B. J. Alder and T. E. Wainwright, “Decay of the velocity autocorrelation function,” Phys. Rev. A 1
1970
Earlier work this paper cites.
M. Suzuki, “Ergodicity, constants of motion, and bounds for susceptibilities,” Physica 51
1971
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M. Takahashi, “Thermodynamics of the Heisenberg-Ising model for | Δ | < 1 |\Delta|<1 in one dimension,” Physics Letters A 36
1971
Earlier work this paper cites.
M. Takahashi, “One-Dimensional Hubbard Model at Finite Temperature,” Progress of Theoretical Physics 47
1972
Earlier work this paper cites.
M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, “Method for Solving the Sine-Gordon Equation,” Phys. Rev. Lett. 30
1973
Earlier work this paper cites.
M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, “The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems,” Studies in Applied Mathematics 53
1974
Earlier work this paper cites.
J. Satsuma and N. Yajima, “B. Initial Value Problems of One-Dimensional Self-Modulation of Nonlinear Waves in Dispersive Media,” Progress of Theoretical Physics Supplement 55
1974
Earlier work this paper cites.
Y. Pomeau and P. Resibois, “Time dependent correlation functions and mode-mode coupling theories,” Physics Reports 19
1975
Earlier work this paper cites.
M. Lakshmanan, T. Ruijgrok, and C. Thompson, “On the dynamics of a continuum spin system,” Physica A: Statistical Mechanics and its Applications 84
1976
Earlier work this paper cites.
H. Nielsen and S. Chadha, “On how to count Goldstone bosons,” Nuclear Physics B 105
1976
Earlier work this paper cites.
L. Takhtajan, “Integration of the continuous Heisenberg spin chain through the inverse scattering method,” Physics Letters A 64
1977
Earlier work this paper cites.
J. C. Hensel and R. C. Dynes, “Interaction of Electron-Hole Drops with Ballistic Phonons in Heat Pulses: The Phonon Wind,” Phys. Rev. Lett. 39
1977
Earlier work this paper cites.
A. B. Zamolodchikov and A. B. Zamolodchikov, “Relativistic factorized S S -matrix in two dimensions having O ( N ) O(N) isotopic symmetry,” Nuclear Physics B 133
1978
Earlier work this paper cites.
M. Lüscher, “Quantum non-local charges and absence of particle production in the two-dimensional non-linear sigma model,” Nuclear Physics B 135
1978
Earlier work this paper cites.
E. Sklyanin, “On complete integrability of the Landau-Lifshitz equation,” (1979)
1979
Earlier work this paper cites.
A. B. Zamolodchikov and A. B. Zamolodchikov, “Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models,” Annals of Physics 120
1979
Earlier work this paper cites.
M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, 1981)
1981
Earlier work this paper cites.
H. van Beijeren, “Transport properties of stochastic Lorentz models,” Rev. Mod. Phys. 54
1982
Earlier work this paper cites.
Seshadri, V. and West, Bruce J., “Fractal dimensionality of lévy processes,” Proceedings of the National Academy of Sciences 79
1982
Earlier work this paper cites.
F. Haldane, “Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model,” Physics Letters A 93
1983
Earlier work this paper cites.
M. Ernst, J. Machta, J. Dorfman, and H. Van Beijeren, “Long time tails in stationary random media. I. Theory,” Journal of statistical physics 34
1984
Earlier work this paper cites.
H. van Beijeren, R. Kutner, and H. Spohn, “Excess noise for driven diffusive systems,” Phys. Rev. Lett. 54
1985
Earlier work this paper cites.
P. Wiegmann, “Exact solution of the O ( 3 ) O(3) nonlinear two-dimensional sigma-model,” JETP Letters 41
1985
Earlier work this paper cites.
M. Kardar, G. Parisi, and Y.-C. Zhang, “Dynamic Scaling of Growing Interfaces,” Phys. Rev. Lett. 56
1986
Earlier work this paper cites.
L. D. Faddeev and L. A. Takhtajan, Hamiltonian Methods in the Theory of Solitons (Springer Berlin Heidelberg, 1987)
1987
Earlier work this paper cites.
M. Steiner, K. Kakurai, J. K. Kjems, D. Petitgrand, and R. Pynn, “Inelastic neutron scattering studies on 1D near‐Heisenberg antiferromagnets: A test of the Haldane conjecture,” Journal of Applied Physics 61
1987
Earlier work this paper cites.
R. M. Morra, W. J. L. Buyers, R. L. Armstrong, and K. Hirakawa, “Spin dynamics and the Haldane gap in the spin-1 quasi-one-dimensional antiferromagnet CsNiCl 3 {\mathrm{CsNiCl}}_{3} ,” Phys. Rev. B 38
1988
Earlier work this paper cites.
B. S. Shastry and B. Sutherland, “Twisted boundary conditions and effective mass in heisenberg-ising and hubbard rings,” Phys. Rev. Lett. 65
1990
Earlier work this paper cites.
J.-P. Bouchaud and A. Georges, “Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications,” Physics Reports 195
1990
Earlier work this paper cites.
R. L. Ricca, “Rediscovery of Da Rios equations,” Nature 352
1991
Earlier work this paper cites.
D. Ertaş and M. Kardar, “Dynamic roughening of directed lines,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
F. H. L. Essler, V. E. Korepin, and K. Schoutens, “New exactly solvable model of strongly correlated electrons motivated by high- T c T_{c} superconductivity,” Phys. Rev. Lett. 68
1992
Earlier work this paper cites.
S. Ma, C. Broholm, D. H. Reich, B. J. Sternlieb, and R. W. Erwin, “Dominance of long-lived excitations in the antiferromagnetic spin-1 chain NENP,” Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
A. Zamolodchikov and A. Zamolodchikov, “Massless factorized scattering and sigma models with topological terms,” Nuclear Physics B 379
1992
Earlier work this paper cites.
V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions (Cambridge University Press, 1993)
1993
Earlier work this paper cites.
P. Deift and X. Zhou, “A Steepest Descent Method for Oscillatory Riemann–Hilbert Problems. Asymptotics for the MKdV Equation,” The Annals of Mathematics 137
1993
Earlier work this paper cites.
P. A. Deift, A. R. Its, and X. Zhou, “Long-time asymptotics for integrable nonlinear wave equations,” in Springer Series in Nonlinear Dynamics (Springer Berlin Heidelberg, 1993) pp. 181–204
1993
Earlier work this paper cites.
X. D. Wu, G. S. Kino, J. T. Fanton, and A. Kapitulnik, “Photothermal microscope for high‐ T c T_{c} superconductors and charge density waves,” Review of Scientific Instruments 64
1993
Earlier work this paper cites.
R. Shankar, “Renormalization-group approach to interacting fermions,” Rev. Mod. Phys. 66
1994
Earlier work this paper cites.
D. Uglov and V. Korepin, “The Yangian symmetry of the Hubbard model,” Physics Letters A 190
1994
Earlier work this paper cites.
I. A. Zaliznyak, L.-P. Regnault, and D. Petitgrand, “Neutron-scattering study of the dynamic spin correlations in CsNiCl 3 {\mathrm{CsNiCl}}_{3} above Néel ordering,” Phys. Rev. B 50
1994
Earlier work this paper cites.
T. Jolicur and O. Golinelli, “ σ \sigma -model study of Haldane-gap antiferromagnets,” Phys. Rev. B 50
1994
Earlier work this paper cites.
H. Castella, X. Zotos, and P. Prelovšek, “Integrability and Ideal Conductance at Finite Temperatures,” Phys. Rev. Lett. 74
1995
Earlier work this paper cites.
S. Weinberg, The quantum theory of fields , Vol. 2 (Cambridge university press, 1995)
1995
Earlier work this paper cites.
X. Zotos and P. Prelovšek, “Evidence for ideal insulating or conducting state in a one-dimensional integrable system,” Phys. Rev. B 53
1996
Earlier work this paper cites.
P. Fendley and H. Saleur, “Nonequilibrium dc noise in a Luttinger liquid with an impurity,” Phys. Rev. B 54
1996
Earlier work this paper cites.
J. Sagi and I. Affleck, “Theory of nuclear magnetic relaxation in Haldane-gap antiferromagnets,” Phys. Rev. B 53
1996
Earlier work this paper cites.
S. Sachdev and K. Damle, “Low Temperature Spin Diffusion in the One-Dimensional Quantum O(3) Nonlinear σ \sigma Model,” Phys. Rev. Lett. 78
1997
Earlier work this paper cites.
X. Zotos, F. Naef, and P. Prelovsek, “Transport and conservation laws,” Phys. Rev. B 55
1997
Earlier work this paper cites.
S. Sachdev and A. P. Young, “Low Temperature Relaxational Dynamics of the Ising Chain in a Transverse Field,” Phys. Rev. Lett. 78
1997
Earlier work this paper cites.
C. Boldrighini and Y. M. Suhov, “One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States,” Communications in Mathematical Physics 189
1997
Earlier work this paper cites.
K. Damle and S. Sachdev, “Nonzero-temperature transport near quantum critical points,” Phys. Rev. B 56
1997
Earlier work this paper cites.
K. Damle and S. Sachdev, “Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures,” Phys. Rev. B 57
1998
Earlier work this paper cites.
B. Narozhny, A. Millis, and N. Andrei, “Transport in the XXZ model,” Phys. Rev. B 58
1998
Earlier work this paper cites.
F. Naef and X. Zotos, “Spin and energy correlations in the one dimensional spin- 1 / 2 1/2 Heisenberg model,” Journal of Physics: Condensed Matter 10
1998
Earlier work this paper cites.
S. Fujimoto and N. Kawakami, “Exact Drude weight for the one-dimensional Hubbard model at finite temperatures,” Journal of Physics A: Mathematical and General 31
1998
Earlier work this paper cites.
T. Koma and B. Nachtergaele, “The complete set of ground states of the ferromagnetic XXZ chains,” Advances in Theoretical and Mathematical Physics 2
1998
Earlier work this paper cites.
S. Lukyanov, “Low energy effective Hamiltonian for the XXZ spin chain,” Nuclear Physics B 522
1998
Earlier work this paper cites.
X. Zotos, “Finite Temperature Drude Weight of the One-Dimensional Spin-1/2 Heisenberg Model,” Phys. Rev. Lett. 82
1999
Earlier work this paper cites.
S. Fujimoto, “Spin Transport Properties of the Quantum One-Dimensional Non-Linear Sigma Model: an Application to Haldane Gap Systems,” Journal of the Physical Society of Japan 68
1999
Earlier work this paper cites.
T. Antal, Z. Rácz, A. Rákos, and G. M. Schütz, “Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles,” Physical Review E 59
1999
Earlier work this paper cites.
M. Bockrath, D. H. Cobden, J. Lu, A. G. Rinzler, R. E. Smalley, L. Balents, and P. L. McEuen, “Luttinger-liquid behaviour in carbon nanotubes,” Nature 397
1999
Earlier work this paper cites.
P. Fendley, “Sigma Models as Perturbed Conformal Field Theories,” Phys. Rev. Lett. 83
1999
Earlier work this paper cites.
A. Rosch and N. Andrei, “Conductivity of a clean one-dimensional wire,” Phys. Rev. Lett. 85
2000
Earlier work this paper cites.
A. Dhar and B. Sriram Shastry, “Bloch Walls and Macroscopic String States in Bethe’s Solution of the Heisenberg Ferromagnetic Linear Chain,” Phys. Rev. Lett. 85
2000
Earlier work this paper cites.
P. Fendley, “Integrable sigma models and perturbed coset models,” Journal of High Energy Physics 2001
2001
Earlier work this paper cites.
J. V. Alvarez and C. Gros, “Low-temperature transport in heisenberg chains,” Phys. Rev. Lett. 88
2002
Earlier work this paper cites.
T. Kirkpatrick, D. Belitz, and J. Sengers, “Long-time tails, weak localization, and classical and quantum critical behavior,” Journal of Statistical Physics 109
2002
Earlier work this paper cites.
M. Oshikawa and I. Affleck, “Electron spin resonance in s = 1 2 s=\frac{1}{2} antiferromagnetic chains,” Phys. Rev. B 65
2002
Earlier work this paper cites.
K. Saito, “Strong evidence of normal heat conduction in a one-dimensional quantum system,” EPL (Europhysics Letters) 61
2003
Earlier work this paper cites.
F. Heidrich-Meisner, A. Honecker, D. Cabra, and W. Brenig, “Zero-frequency transport properties of one-dimensional spin-1 2 systems,” Phys. Rev. B 68
2003
Earlier work this paper cites.
S. Gutiérrez, J. Rivas, and L. Vega, “Formation of singularities and self-similar vortex motion under the localized induction approximation,” Communications in Partial Differential Equations 28
2003
Earlier work this paper cites.
T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, 2003) Chap. 6
2003
Earlier work this paper cites.
E. Shimshoni, N. Andrei, and A. Rosch, “Thermal conductivity of spin- 1 2 \frac{1}{2} chains,” Phys. Rev. B 68
2003
Earlier work this paper cites.
R. M. Konik, “Haldane-gapped spin chains: Exact low-temperature expansions of correlation functions,” Phys. Rev. B 68
2003
Earlier work this paper cites.
F. Göhmann, A. Klümper, and A. Seel, “Integral representations for correlation functions of the XXZ chain at finite temperature,” Journal of Physics A: Mathematical and General 37
2004
Earlier work this paper cites.
B. Stefanski and A. Tseytlin, “Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations,” Journal of High Energy Physics 2004
2004
Earlier work this paper cites.
V. A. Kazakov, A. Marshakov, J. A. Minahan, and K. Zarembo, “Classical/quantum integrability in AdS/CFT,” Journal of High Energy Physics 2004
2004
Earlier work this paper cites.
J. Karadamoglou and X. Zotos, “Diffusive transport in spin-1 chains at high temperatures,” Phys. Rev. Lett. 93
2004
Cited alongside, same era.
M. Prähofer and H. Spohn, “Exact Scaling Functions for One-Dimensional Stationary KPZ Growth,” Journal of Statistical Physics 115
2004
Cited alongside, same era.
M. Takahashi, Thermodynamics of one-dimensional solvable models (Cambridge university press, 2005)
2005
Cited alongside, same era.
J. Benz, T. Fukui, A. Klümper, and C. Scheeren, “On the Finite Temperature Drude Weight of the Anisotropic Heisenberg Chain,” Journal of the Physical Society of Japan 74
2005
Cited alongside, same era.
Fabian H. L. Essler and Holger Frahm and Frank Göhmann and Andreas Klümper and Vladimir E. Korepin, The One-Dimensional Hubbard Model (Cambridge University Press (CUP), 2005)
2005
Cited alongside, same era.
R. J. Sánchez and V. K. Varma, “Finite-size anomalies of the Drude weight: Role of symmetries and ensembles,” Phys. Rev. B 96
2017
Later among the works it cites.
V. Alba and P. Calabrese, “Entanglement and thermodynamics after a quantum quench in integrable systems,” Proceedings of the National Academy of Sciences 114
2017
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L. Piroli, J. De Nardis, M. Collura, B. Bertini, and M. Fagotti, “Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions,” Phys. Rev. B 96
2017
Later among the works it cites.
R. Steinigeweg, F. Jin, H. De Raedt, K. Michielsen, and J. Gemmer, “Charge diffusion in the one-dimensional Hubbard model,” Physical Review E 96
2017
Later among the works it cites.
A. De Luca, M. Collura, and J. De Nardis, “Nonequilibrium spin transport in integrable spin chains: Persistent currents and emergence of magnetic domains,” Phys. Rev. B 96
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D. Gobert, C. Kollath, U. Schollwöck, and G. Schütz, “Real-time dynamics in spin- 1 / 2 1/2 chains with adaptive time-dependent density matrix renormalization group,” Physical Review E 71
2005
Cited alongside, same era.
A. Rosch, “Optical conductivity of clean metals,” Annalen der Physik 15
2006
Cited alongside, same era.
J. L. Vázquez, Smoothing and decay estimates for nonlinear diffusion equations: equations of porous medium type , Vol. 33 (Oxford University Press, 2006)
2006
Cited alongside, same era.
N. Beisert, V. Kazakov, and K. Sakai, “Algebraic Curve for the SO(6) Sector of AdS/CFT,” Communications in Mathematical Physics 263
2006
Cited alongside, same era.
N. Beisert, V. Kazakov, K. Sakai, and K. Zarembo, “The Algebraic Curve of Classical Superstrings on A d S 5 × S 5 AdS_{5}\times S_{5} ,” Communications in Mathematical Physics 263
2006
Cited alongside, same era.
T. Masuda, A. Zheludev, H. Manaka, L.-P. Regnault, J.-H. Chung, and Y. Qiu, “Dynamics of Composite Haldane Spin Chains in IPA − CuCl 3 \mathrm{IPA}\mathrm{\text{$-$}}{\mathrm{CuCl}}_{3} ,” Phys. Rev. Lett. 96
2006
Cited alongside, same era.
J. L. Vázquez, The porous medium equation: mathematical theory (Oxford University Press on Demand, 2007)
2007
Cited alongside, same era.
2017
Later among the works it cites.
G. Misguich, K. Mallick, and P. L. Krapivsky, “Dynamics of the spin- 1 2 \frac{1}{2} Heisenberg chain initialized in a domain-wall state,” Phys. Rev. B 96
2017
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J.-M. Stéphan, “Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain,” Journal of Statistical Mechanics: Theory and Experiment 2017
2017
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B. Doyon, T. Yoshimura, and J.-S. Caux, “Soliton gases and generalized hydrodynamics,” Phys. Rev. Lett. 120
2018
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V. B. Bulchandani, R. Vasseur, C. Karrasch, and J. E. Moore, “Bethe-Boltzmann hydrodynamics and spin transport in the XXZ chain,” Phys. Rev. B 97
2018
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M. Vanicat, L. Zadnik, and T. Prosen, “Integrable Trotterization: Local Conservation Laws and Boundary Driving,” Phys. Rev. Lett. 121
2018
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E. Ilievski, J. De Nardis, M. Medenjak, and T. Prosen, “Superdiffusion in one-dimensional quantum lattice models,” Phys. Rev. Lett. 121
2018
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M. Collura, A. De Luca, and J. Viti, “Analytic solution of the domain-wall nonequilibrium stationary state,” Phys. Rev. B 97
2018
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M. Lebrat, P. Grišins, D. Husmann, S. Häusler, L. Corman, T. Giamarchi, J.-P. Brantut, and T. Esslinger, “Band and correlated insulators of cold fermions in a mesoscopic lattice,” Phys. Rev. X 8
2018
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D. Forster, Hydrodynamic fluctuations, broken symmetry, and correlation functions (CRC Press, 2018)
2018
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D. Pines, Theory of Quantum Liquids: Normal Fermi Liquids (CRC Press, 2018)
2018
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J. De Nardis, D. Bernard, and B. Doyon, “Hydrodynamic diffusion in integrable systems,” Phys. Rev. Lett. 121
2018
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S. Gopalakrishnan, D. A. Huse, V. Khemani, and R. Vasseur, “Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems,” Phys. Rev. B 98
2018
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S. Gopalakrishnan, “Operator growth and eigenstate entanglement in an interacting integrable Floquet system,” Phys. Rev. B 98
2018
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H. Spohn, “Interacting and noninteracting integrable systems,” Journal of Mathematical Physics 59
2018
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F. H. L. Essler, R. van den Berg, and V. Gritsev, “Integrable spin chains with random interactions,” Phys. Rev. B 98
2018
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X. Cao, V. B. Bulchandani, and J. E. Moore, “Incomplete thermalization from trap-induced integrability breaking: Lessons from classical hard rods,” Phys. Rev. Lett. 120
2018
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Y. Tang, W. Kao, K.-Y. Li, S. Seo, K. Mallayya, M. Rigol, S. Gopalakrishnan, and B. L. Lev, “Thermalization near Integrability in a Dipolar Quantum Newton’s Cradle,” Phys. Rev. X 8
2018
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M. Schemmer, I. Bouchoule, B. Doyon, and J. Dubail, “Generalized hydrodynamics on an atom chip,” Phys. Rev. Lett. 122
2019
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A. Urichuk, Y. Öz, A. Klümper, and J. Sirker, “The spin Drude weight of the XXZ chain and generalized hydrodynamics,” SciPost Phys. 6
2019
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M. Ljubotina, M. Žnidarič, and T. Prosen, “Kardar-Parisi-Zhang Physics in the Quantum Heisenberg Magnet,” Phys. Rev. Lett. 122
2019
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A. Das, M. Kulkarni, H. Spohn, and A. Dhar, “Kardar-Parisi-Zhang scaling for an integrable lattice Landau-Lifshitz spin chain,” Phys. Rev. E 100
2019
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S. Gopalakrishnan and R. Vasseur, “Kinetic Theory of Spin Diffusion and Superdiffusion in X X Z XXZ Spin Chains,” Phys. Rev. Lett. 122
2019
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J. De Nardis, M. Medenjak, C. Karrasch, and E. Ilievski, “Anomalous spin diffusion in one-dimensional antiferromagnets,” Phys. Rev. Lett. 123
2019
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S. Gopalakrishnan, R. Vasseur, and B. Ware, “Anomalous relaxation and the high-temperature structure factor of XXZ spin chains,” Proceedings of the National Academy of Sciences 116
2019
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M. Ljubotina, L. Zadnik, and T. Prosen, “Ballistic spin transport in a periodically driven integrable quantum system,” Phys. Rev. Lett. 122
2019
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M. A. Nichols, L. W. Cheuk, M. Okan, T. R. Hartke, E. Mendez, T. Senthil, E. Khatami, H. Zhang, and M. W. Zwierlein, “Spin transport in a Mott insulator of ultracold fermions,” Science 363
2019
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J. De Nardis, D. Bernard, and B. Doyon, “Diffusion in generalized hydrodynamics and quasiparticle scattering,” SciPost Phys. 6
2019
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K. Klobas, M. Medenjak, T. Prosen, and M. Vanicat, “Time-dependent matrix product ansatz for interacting reversible dynamics,” Communications in Mathematical Physics 371
2019
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A. Dhar, A. Kundu, and A. Kundu, “Anomalous heat transport in one dimensional systems: A description using non-local fractional-type diffusion equation,” Frontiers in Physics 7
2019
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U. Agrawal, S. Gopalakrishnan, and R. Vasseur, “Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains,” Phys. Rev. B 99
2019
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P. J. D. Crowley, C. R. Laumann, and S. Gopalakrishnan, “Quantum criticality in Ising chains with random hyperuniform couplings,” Phys. Rev. B 100
2019
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E. Ilievski and E. Quinn, “The equilibrium landscape of the Heisenberg spin chain,” SciPost Phys. 7
2019
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V. Alba and P. Calabrese, “Quantum information scrambling after a quantum quench,” Phys. Rev. B 100
2019
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A. Biella, M. Collura, D. Rossini, A. De Luca, and L. Mazza, “Ballistic transport and boundary resistances in inhomogeneous quantum spin chains,” Nature communications 10
2019
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V. B. Bulchandani and C. Karrasch, “Subdiffusive front scaling in interacting integrable models,” Phys. Rev. B 99
2019
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J.-M. Stéphan, “Free fermions at the edge of interacting systems,” SciPost Phys. 6
2019
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G. Misguich, N. Pavloff, and V. Pasquier, “Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point,” SciPost Phys. 7
2019
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O. Gamayun, Y. Miao, and E. Ilievski, “Domain-wall dynamics in the Landau-Lifshitz magnet and the classical-quantum correspondence for spin transport,” Phys. Rev. B 99
2019
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O. Gamayun and O. Lisovyy, “On self-similar solutions of the vortex filament equation,” Journal of Mathematical Physics 60
2019
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S. Capponi, M. Dupont, A. W. Sandvik, and P. Sengupta, “NMR relaxation in the spin-1 Heisenberg chain,” Phys. Rev. B 100
2019
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K. Mallayya, M. Rigol, and W. De Roeck, “Prethermalization and thermalization in isolated quantum systems,” Phys. Rev. X 9
2019
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T. LeBlond, K. Mallayya, L. Vidmar, and M. Rigol, “Entanglement and matrix elements of observables in interacting integrable systems,” Physical Review E 100
2019
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E. Granet and F. H. Essler, “A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model,” Scipost Phys. 9
2020
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A. C. Cubero and M. Panfil, “Generalized hydrodynamics regime from the thermodynamic bootstrap program,” SciPost Phys. 8
2020
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B. Doyon, “Lecture Notes On Generalised Hydrodynamics,” SciPost Phys. Lect. Notes , 18 (2020)
2020
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S. Gopalakrishnan and S. Parameswaran, “Dynamics and transport at the threshold of many-body localization,” Physics Reports 862
2020
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A. Das, K. Damle, A. Dhar, D. A. Huse, M. Kulkarni, C. B. Mendl, and H. Spohn, “Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain,” Journal of Statistical Physics 180
2020
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M. Dupont and J. E. Moore, “Universal spin dynamics in infinite-temperature one-dimensional quantum magnets,” Phys. Rev. B 101
2020
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F. Weiner, P. Schmitteckert, S. Bera, and F. Evers, “High-temperature spin dynamics in the Heisenberg chain: Magnon propagation and emerging Kardar-Parisi-Zhang scaling in the zero-magnetization limit,” Phys. Rev. B 101
2020
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Ž. Krajnik and T. Prosen, “Kardar–Parisi–Zhang Physics in Integrable Rotationally Symmetric Dynamics on Discrete Space–Time Lattice,” Journal of Statistical Physics 179
2020
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M. Fava, B. Ware, S. Gopalakrishnan, R. Vasseur, and S. A. Parameswaran, “Spin crossovers and superdiffusion in the one-dimensional Hubbard model,” Phys. Rev. B 102
2020
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2020
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