Emergent hydrodynamics in integrable quantum systems out of equilibrium

By O. Castro-Alvaredo, B. Doyon, T. Yoshimura. 2016

601 citations recorded by the source corpus.

Understanding the general principles underlying strongly interacting quantum states out of equilibrium is one of the most important tasks of current theoretical physics. With experiments accessing the intricate dynamics of many-body quantum systems, it is paramount to develop powerful methods that encode the emergent physics. Up to now, the strong dichotomy observed between integrable and non-integrable evolutions made an overarching theory difficult to build, especially for transport phenomena where space-time profiles are drastically different. We present a novel framework for studying transport in integrable systems: hydrodynamics with infinitely-many conservation laws. This bridges the conceptual gap between integrable and non-integrable quantum dynamics, and gives powerful tools for accurate studies of space-time profiles. We apply it to the description of energy transport between heat baths, and provide a full description of the current-carrying non-equilibrium steady state and the transition regions in a family of models including the Lieb-Liniger model of interacting Bose gases, realized in experiments.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dc1fcdc015414555f4995411e41c8bb86ef2b797

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

A note on generalized hydrodynamics: inhomogeneous fields and other concepts (2016, background): “In [19], it was shown, in general diagonal-scattering integrable models of quantum field theory including the Lieb-Liniger and sinh-Gordon models, that the infinite system of conservation laws – for the infinite number of GGE potentials – can be recast into a system of hydrodynamic equations for qua”
Entanglement in a fermion chain under continuous monitoring (2018, background): “GHD has been successfully developed as a large-scale description of the non-equilibrium dynamics of Bethe-integrable systems, both free and interacting [45–48].”
Detection of Kardar–Parisi–Zhang hydrodynamics in a quantum Heisenberg spin-1/2 chain (2020, background): “results A quantitative test to distinguish different kinds of hydrodynamics is to examine the scattering intensity behaviour at small energy versus Q near the ferromagnetic wavevector Q = 0 (equation (2)).”
Diffusion in generalized hydrodynamics and quasiparticle scattering (2018, background): “7) This agrees with the general TBA structure used in GHD, see [49,50].”
Lecture notes on Generalised Hydrodynamics (2019, methodology): “In interacting, integrable, non-conformal quantum models, the full solution was provided in [1] for field theories, with the examples of the sinh-Gordon and Lieb-Liniger models, and in [2] for quantum chains, with the example of the XXZ anisotropic Heisenberg chain.”
Conformal Field Theory for Inhomogeneous One-dimensional Quantum Systems: the Example of Non-Interacting Fermi Gases (2016, background): “The key assumption of our work is separation of scales: the system is locally homogeneous (but only locally), which is also the working limit of all approaches constructed so far [47, 49, 50].”
Theoretical foundations of quantum hydrodynamics for plasmas (2017, background): “have the same form, but n and w must be understood as quantities that are averaged over the grand ensemble [50, 51].”
Drude Weight for the Lieb-Liniger Bose Gas (2017, methodology): “In [38, 39], the spin-spin Drude weight was exactly evaluated by combining the hydrodynamic techniques of [3, 4] with a formula expressing it as a linear response of the non-equilibrium current to a change of driving potential [37, 40, 41].”