Emergent hydrodynamics in integrable quantum systems out of equilibrium
TL;DR: In this article, the authors present a framework for studying transport in integrable systems: hydrodynamics with infinitely many conservation laws, which bridges the conceptual gap between integrably and non-integrably quantum dynamics, and gives powerful tools for accurate studies of space-time profiles.
Abstract: 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.
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TL;DR: In this paper, the authors review the structure of the conservation laws in noninteracting spin chains and unveil a formal expression for the corresponding currents, and explore the effects of a localized defect.
Abstract: We review the structure of the conservation laws in noninteracting spin chains and unveil a formal expression for the corresponding currents. We briefly discuss how interactions affect the picture. In the second part, we explore the effects of a localized defect. We show that the emergence of spontaneous currents near the defect undermines any description of the late-time dynamics by means of a stationary state in a finite chain. In particular, the diagonal ensemble does not work. Finally, we provide numerical evidence that simple generic localized defects are not sufficient to induce thermalization.
56 citations
TL;DR: In this article, a kinetic equation of Bethe-Boltzmann type for the distribution function of conserved quasiparticles is derived for the quantum and classical Toda lattice models.
Abstract: We consider the kinetic theory of the quantum and classical Toda lattice models. A kinetic equation of Bethe-Boltzmann type is derived for the distribution function of conserved quasiparticles. Near the classical limit, we show that the kinetic theory depends smoothly on Planck's constant, and explicitly characterise the leading quantum corrections to classical behaviour. The classical kinetic theory is compared with direct numerical simulations and shows excellent agreement. Finally, we connect the Bethe-Boltzmann approach with the classical inverse scattering method, by identifying conserved quasiparticles with the spectrum of the Lax matrix.
33 citations
TL;DR: In this paper, the authors review the structure of the conservation laws in noninteracting spin chains and unveil a formal expression for the corresponding currents, and explore the effects of a localized defect.
Abstract: We review the structure of the conservation laws in noninteracting spin chains and unveil a formal expression for the corresponding currents. We briefly discuss how interactions affect the picture. In the second part, we explore the effects of a localized defect. We show that the emergence of spontaneous currents near the defect undermines any description of the late-time dynamics by means of a stationary state in a finite chain. In particular, the diagonal ensemble does not work. Finally, we provide numerical evidence that simple generic localized defects are not sufficient to induce thermalization.
26 citations
TL;DR: In this article, the density-density correlation function of the 1D Lieb-Liniger model was studied and an exact expression for the small momentum limit of the static correlator in the thermodynamic limit was obtained.
Abstract: We study the density-density correlation function of the 1D Lieb-Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We achieve this by summing exactly over the relevant form factors of the density operator in the small momentum limit. The result is valid for any eigenstate, including thermal and non-thermal states. We also show that the small momentum limit of the dynamic structure factors obeys a generalized detailed balance relation valid for any equilibrium state.
25 citations
TL;DR: In this article, the Bessel kernel was used to analyze the fluctuations of the spin current for the one dimensional XX spin chain starting from the domain wall initial condition, and an exact analytical expression for the large deviation function was obtained by applying the Coulomb gas method.
Abstract: We investigate the fluctuations of the spin current for the one dimensional XX spin chain starting from the domain wall initial condition. The generating function of the current is shown to be written as a determinant with the Bessel kernel. An exact analytical expression for the large deviation function is obtained by applying the Coulomb gas method. Our results are also compared with DMRG calculations.
24 citations