# Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model

## Abstract

Here, we consider the construction of a generalized Gibbs ensemble composed of complete bases of conserved charges in the repulsive Lieb-Liniger model. We will show that it is possible to construct these bases with varying locality as well as demonstrating that such constructions are always possible provided one has in hand at least one complete basis set of charges. This procedure enables the construction of bases of charges that possess well-defined, finite expectation values given an arbitrary initial state. We demonstrate the use of these charges in the context of two different quantum quenches: a quench where the strength of the interactions in a one-dimensional gas is switched suddenly from zero to some finite value and the release of a one-dimensional cold atomic gas from a confining parabolic trap. While we focus on the Lieb-Liniger model in this paper, the principle of the construction of these charges applies to all integrable models, both in continuum and lattice form.

- Authors:

- Brookhaven National Lab. (BNL), Upton, NY (United States)

- 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:
- 1489349

- Alternate Identifier(s):
- OSTI ID: 1483031

- Report Number(s):
- BNL-210827-2018-JAAM

Journal ID: ISSN 2470-0045; PLEEE8

- Grant/Contract Number:
- SC0012704

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review E

- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 5; Journal ID: ISSN 2470-0045

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Palmai, Tamas, and Konik, R. M.
```*Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevE.98.052126.

```
Palmai, Tamas, & Konik, R. M.
```*Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model*. United States. doi:10.1103/PhysRevE.98.052126.

```
Palmai, Tamas, and Konik, R. M. Wed .
"Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model". United States. doi:10.1103/PhysRevE.98.052126.
```

```
@article{osti_1489349,
```

title = {Quasilocal charges and the generalized Gibbs ensemble in the Lieb-Liniger model},

author = {Palmai, Tamas and Konik, R. M.},

abstractNote = {Here, we consider the construction of a generalized Gibbs ensemble composed of complete bases of conserved charges in the repulsive Lieb-Liniger model. We will show that it is possible to construct these bases with varying locality as well as demonstrating that such constructions are always possible provided one has in hand at least one complete basis set of charges. This procedure enables the construction of bases of charges that possess well-defined, finite expectation values given an arbitrary initial state. We demonstrate the use of these charges in the context of two different quantum quenches: a quench where the strength of the interactions in a one-dimensional gas is switched suddenly from zero to some finite value and the release of a one-dimensional cold atomic gas from a confining parabolic trap. While we focus on the Lieb-Liniger model in this paper, the principle of the construction of these charges applies to all integrable models, both in continuum and lattice form.},

doi = {10.1103/PhysRevE.98.052126},

journal = {Physical Review E},

issn = {2470-0045},

number = 5,

volume = 98,

place = {United States},

year = {2018},

month = {11}

}