Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions
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In this article, a generalized hydrodynamic description applies, according to which the system can locally be represented by space-and time-dependent stationary states, where magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamics equations.Abstract:
We consider the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joined together At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time-dependent stationary states The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamic equations and which signal nonballistic spin transport We ascribe this phenomenon to the structure of the local conservation laws and make a prediction for the exact location of the jumps We find that the jumps propagate at the velocities of the heaviest quasiparticles By means of time-dependent density matrix renormalization group simulations we show that our theory yields a complete description of the long-time steady profiles of conserved charges, currents, and local correlationsread more
Citations
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Quantum Inverse Scattering Method and Correlation Functions
TL;DR: One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References as discussed by the authors
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Generalized Hydrodynamics on an Atom Chip
TL;DR: The measurements, performed on weakly interacting atomic clouds that lie at the crossover between the quasicondensate and the ideal Bose gas regimes, are in very good agreement with the theory, and contrasts with the previously existing "conventional" hydrodynamic approach.
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Hydrodynamic Diffusion in Integrable Systems.
TL;DR: It is shown that hydrodynamic diffusion is generically present in many-body, one-dimensional interacting quantum and classical integrable models, and extended to terms of Navier-Stokes type, which leads to positive entropy production and diffusive relaxation mechanisms.
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Finite-temperature transport in one-dimensional quantum lattice models
Bruno Bertini,Fabian Heidrich-Meisner,Christoph Karrasch,Tomaž Prosen,Robin Steinigeweg,Marko Žnidarič +5 more
TL;DR: In this paper, a review of the current understanding of transport in one-dimensional lattice models, in particular in the paradigmatic example of the spin-1/2 XXZ and Fermi-Hubbard models, is reviewed, as well as state-of-theart theoretical methods, including both analytical and computational approaches.
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Entanglement dynamics after quantum quenches in generic integrable systems
Vincenzo Alba,Pasquale Calabrese +1 more
TL;DR: In this paper, the exact time dependence of entanglement entropy in non-equilibrium quantum systems is derived by combining a quasiparticle picture with the exact knowledge of the stationary state provided by Bethe ansatz.
References
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Quantum Inverse Scattering Method and Correlation Functions
TL;DR: One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References as discussed by the authors
MonographDOI
The one-dimensional Hubbard model
TL;DR: In this article, the authors present an algebraic approach to the Hubbard model and a path integral approach to thermodynamics, as well as the Yangian symmetry of the model in the infinite interval limit.