# Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics

## TL;DR

This paper demonstrates that generalized hydrodynamics (GHD) provides a more accurate and comprehensive description of one-dimensional Bose gases than conventional hydrodynamics (CHD), especially in the presence of sharp profiles and at nonzero temperatures.

## Contribution

The authors establish that GHD supersedes CHD for 1D Bose gases, justifies GHD from hydrodynamic principles, and numerically confirm its accuracy across the full interaction range.

## Key findings

- GHD reduces to CHD at zero temperature without shocks.
- Sharp profiles in CHD dissolve into GHD's hierarchy, avoiding shocks.
- Numerical simulations confirm GHD's accuracy at zero temperature.

## 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.