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

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.

Front dynamics and entanglement in the XXZ chain with a gradient

“…The question is, however, if the occupation functions characterized by a single Fermi sea would be stable under such an advective evolution. In fact, in a recent study of the Lieb-Liniger model with an inhomogeneous initial density profile [17], it has been pointed out that instabilities are likely to occur, leading to a breakup of the Fermi sea into several disconnected parts. Whether this would also occur for the gradient XXZ chain at hand is clearly a very interesting open question which deserves further studies.…”

“…Starting from an inhomogeneous initial state, the method has been very successful in describing the time-evolved profiles of various observables (e.g. spin or energy densities and currents) in a hydrodynamic scaling regime, for a number of different situations and model systems [13][14][15][16][17][18][19][20][21].…”

High-temperature spin dynamics in the Heisenberg chain: Magnon propagation and emerging Kardar-Parisi-Zhang scaling in the zero-magnetization limit

“…Diffusive corrections and entropy-production due to quasi-particle scattering have been incorporated recently [6,7]. Moreover, quantum hydrodynamics for one-dimensional systems at zero temperature developed earlier [8,9], formulated in terms of density and velocity fields, was shown to be reproduced by GHD in the corresponding limit [10].…”

Higher-order generalized hydrodynamics in one dimension: The noninteracting test

“…The framework developed in Refs [48,49] is now known as generalized hydrodynamics [48], where "generalized" is used to emphasize that integrable models have infinitely many (quasi)local charges [50]. We will generally omit "generalized" and refer to the system of equations derived in [48,49] as first-order hydrodynamics, 1 st GHD, to emphasize that it is a system of first-order partial differential equations.Within 1 st GHD, it was possible to compute the profiles of local observables [48,49,[51][52][53][54][55][56][57], to conjecture an expression for the time evolution of the entanglement entropy [58], and to efficiently calculate Drude weights [59][60][61][62][63]. There are however fundamental questions that can not be addressed within 1 st GHD; diffusive transport [64][65][66][67][68][69] and large-time corrections [20][21][22][23] are two of them.…”