# 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. Here, 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- ormore »

- Authors:

- King’s College London, Strand, London (United Kingdom)
- Univ. de Lorraine, Vandoeuvre-lès-Nancy (France)
- Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Division

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1462405

- Alternate Identifier(s):
- OSTI ID: 1408183

- Report Number(s):
- BNL-207874-2018-JAAM

Journal ID: ISSN 0031-9007; PRLTAO

- Grant/Contract Number:
- SC0012704; AC02-98CH10886

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 119; Journal Issue: 19; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Doyon, Benjamin, Dubail, Jerome, Konik, Robert, and Yoshimura, Takato.
```*Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevLett.119.195301.

```
Doyon, Benjamin, Dubail, Jerome, Konik, Robert, & Yoshimura, Takato.
```*Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics*. United States. doi:10.1103/PhysRevLett.119.195301.

```
Doyon, Benjamin, Dubail, Jerome, Konik, Robert, and Yoshimura, Takato. Wed .
"Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics". United States. doi:10.1103/PhysRevLett.119.195301. https://www.osti.gov/servlets/purl/1462405.
```

```
@article{osti_1462405,
```

title = {Large-Scale Description of Interacting One-Dimensional Bose Gases: Generalized Hydrodynamics Supersedes Conventional Hydrodynamics},

author = {Doyon, Benjamin and Dubail, Jerome and Konik, Robert and Yoshimura, Takato},

abstractNote = {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. Here, 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},

journal = {Physical Review Letters},

issn = {0031-9007},

number = 19,

volume = 119,

place = {United States},

year = {2017},

month = {11}

}

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