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arXiv:1704.04151 · Physical Review Letters

Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics

Benjamin Doyon, Jérôme Dubail, Robert Konik, Takato Yoshimura

Published Nov 7, 2017• 222 citations
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Abstract

The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this Letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying "nonlinear sound waves" emanating from initial density accumulations in the Lieb-Liniger model. We show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-abacus algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.

DOI
10.1103/physrevlett.119.195301

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The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. In this Letter, we show that it supersedes the widely used conventional hydrodynamics (CHD) of one-dimensional Bose gases. We illustrate this by studying "nonlinear sound waves" emanating from initial density accumulations in the Lieb-Liniger model. We show that, at zero temperature and in the absence of shocks, GHD reduces to CHD, thus for the first time justifying its use from purely hydrodynamic principles. We show that sharp profiles, which appear in finite times in CHD, immediately dissolve into a higher hierarchy of reductions of GHD, with no sustained shock. CHD thereon fails to capture the correct hydrodynamics. We establish the correct hydrodynamic equations, which are finite-dimensional reductions of GHD characterized by multiple, disjoint Fermi seas. We further verify that at nonzero temperature, CHD fails at all nonzero times. Finally, we numerically confirm the emergence of hydrodynamics at zero temperature by comparing its predictions with a full quantum simulation performed using the NRG-TSA-abacus algorithm. The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.
The theory of generalized hydrodynamics (GHD) was recently developed as a new tool for the study of inhomogeneous time evolution in many-body interacting systems with infinitely many conserved charges. It offers a full and efficient framework to capture the long-wavelengths nonequilibrium dynamics in experimentally realizable one-dimensional systems, like Bose gases with delta repulsion. In this letter, we study the nonlinear sound waves emanating from initial density accumulations in the zero-temperature Bose gas. We numerically confirm the emergence of GHD by comparing its predictions with a full quantum simulation performed using the NRG-TSA-ABACUS algorithm. We prove that at zero temperature, GHD is equivalent to conventional Galilean hydrodynamics with nontrivial equations of state. We further predict, at long wavelengths and large densities, the appearance of sharp profiles in finite times, that immediately dissolve (no sustained shocks). The analysis is performed in the full interaction range, and is not restricted to either weak- or strong-repulsion regimes.
The results of benchmarks of the recent theory of generalized hydrodynamics (GHD) in the context of the dynamics of the 1D Bose gas described by the Lieb-Liniger model are reported. Through comparisons against several alternative, well-established computational approaches, the range of applicability of GHD in some of the most challenging out-of-equilibrium scenarios, such as propagation of quantum shock waves and collisional relaxation, is verified and validated and, additionally, some of the methods limitations are pointed out.
Generalized hydrodynamics (GHD) is a recent theoretical approach that is becoming a go-to tool for characterizing out-of-equilibrium phenomena in integrable and near-integrable quantum many-body systems. Here, we benchmark its performance against an array of alternative theoretical methods, for an interacting one-dimensional Bose gas described by the Lieb-Liniger model. In particular, we study the evolution of both a localized density bump and dip, along with a quantum Newton's cradle setup, for various interaction strengths and initial equilibrium temperatures. We find that GHD generally performs very well at sufficiently high temperatures or strong interactions. For low temperatures and weak interactions, we highlight situations where GHD, while not capturing interference phenomena on short lengthscales, can describe a coarse-grained behaviour based on convolution averaging that mimics finite imaging resolution in ultracold atom experiments. In a quantum Newton's cradle setup based on a double-well to single-well trap quench, we find that GHD with diffusive corrections demonstrates excellent agreement with the predictions of a classical field approach.
Abstract We review the recent theoretical and experimental progress regarding the generalized hydrodynamics (GHD) behavior of the one-dimensional (1D) Bose gas with contact repulsive interactions, also known as the Lieb–Liniger gas. In the first section, we review the theory of the Lieb–Liniger gas, introducing the key notions of the rapidities and of the rapidity distribution. The latter characterizes the Lieb–Liniger gas after relaxation and is at the heart of GHD. We also present the asymptotic regimes of the Lieb–Liniger gas with their dedicated approximate descriptions. In the second section we enter the core of the subject and review the theoretical results of GHD in 1D Bose gases. The third and fourth sections are dedicated to experimental results obtained in cold atom experiments: the experimental realization of the Lieb–Liniger model is presented in section 3, with a selection of key results for systems at equilibrium, and section 4 presents the experimental tests of the GHD theory. In section 5 we review the effects of atom losses, which, assuming slow loss processes, can be described within the GHD framework. We conclude with a few open questions.
The dynamics of strongly interacting many-body quantum systems are notoriously complex and difficult to simulate. A recently proposed theory called generalized hydrodynamics (GHD) promises to efficiently accomplish such simulations for nearly integrable systems. We test GHD with bundles of ultracold one-dimensional (1D) Bose gases by performing large trap quenches in both the strong and intermediate coupling regimes. We find that theory and experiment agree well over dozens of trap oscillations, for average dimensionless coupling strengths that range from 0.3 to 9.3. Our results show that GHD can accurately describe the quantum dynamics of a 1D nearly integrable experimental system even when particle numbers are low and density changes are large and fast.
Generalized hydrodynamics (GHD) was proposed recently as a formulation of hydrodynamics for integrable systems, taking into account infinitely-many conservation laws. In this note we further develop the theory in various directions. By extending GHD to all commuting flows of the integrable model, we provide a full description of how to take into account weakly varying force fields, temperature fields and other inhomogeneous external fields within GHD. We expect this can be used, for instance, to characterize the non-equilibrium dynamics of one-dimensional Bose gases in trap potentials. We further show how the equations of state at the core of GHD follow from the continuity relation for entropy, and we show how to recover Euler-like equations and discuss possible viscosity terms.