Understanding many-body physics in one dimension from the Lieb-Liniger model

doi:10.1088/1674-1056/24/5/050311

Abstract

This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb- Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe's hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb-Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang-Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb-Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability.

Keywords: many-body physics Lieb-Liniger model

Received: 13 January 2015
Revised: 22 February 2015
Accepted manuscript online:

PACS:	03.75.Ss	(Degenerate Fermi gases)
	71.10.Pm	(Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.))
	02.30.Ik	(Integrable systems)

Fund:

Project supported by the National Basic Research Program of China (Grant No. 2012CB922101) and the National Natural Science Foundation of China (Grant Nos. 11374331 and 11304357).

Corresponding Authors: Guan Xi-Wen
E-mail: xwe105@wipm.ac.cn

About author: 2015-4-17

Cite this article:

Jiang Yu-Zhu (姜玉铸), Chen Yang-Yang (陈洋洋), Guan Xi-Wen (管习文) Understanding many-body physics in one dimension from the Lieb-Liniger model 2015 Chin. Phys. B 24 050311

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