Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0602468 · Journal of Statistical Mechanics Theory and Experiment

Three-body local correlation function in the Lieb–Liniger model: bosonization approach

Vadim Cheianov, H. Smith, Mikhail B. Zvonarev

Published Aug 21, 2006• 41 citations
arXivHTMLPDF

Abstract

We develop a method to calculate vacuum expectation values of local operators in the Lieb–Liniger model. This method is based on a set of new identities obtained using integrability and effective theory ('bosonization') description. We use this method to get an explicit expression for the three-body local correlation function, measured in a recent experiment.

DOI
10.1088/1742-5468/2006/08/p08015

Related papers

Correlation functions of a Lieb–Liniger Bose gas

G. E. Astrakharchik, S. Giorgini

The ground-state correlation functions of a one-dimensional homogeneous Bose system described by the Lieb-Liniger Hamiltonian are investigated by using exact quantum Monte Carlo techniques. This article is an extension of a previous study published in Phys. Rev. A {\bf 68}, 031602 (2003). New results on the local three-body correlator as a function of the interaction strength are included and compared with the measured value from three-body loss experiments. We also carry out a thorough study of the short- and long-range behavior of the one-body density matrix.

arXiv:cond-mat/0510463•Journal of Physics B Atomic Molecular and Optical Physics•May 2, 2006•45 citations

Expectation Values in the Lieb-Liniger Bose Gas

Márton Kormos, Giuseppe Mussardo, Andrea Trombettoni

We present a novel method to compute expectation values in the Lieb-Liniger model both at zero and finite temperature. These quantities, relevant in the physics of one-dimensional ultracold Bose gases, are expressed by a series that has a remarkable behavior of convergence. Among other results, we show the computation of the three-body expectation value at finite temperature, a quantity that rules the recombination rate of the Bose gas.

arXiv:0909.1336•Physical Review Letters•Nov 20, 2009•98 citations

Three-Body Correlation Functions and Recombination Rates for Bosons in Three Dimensions and One Dimension

Elmar Haller, Mohamed Rabie, Manfred J. Mark +5 more

We investigate local three-body correlations for bosonic particles in three dimensions and one dimension as a function of the interaction strength. The three-body correlation function g(3) is determined by measuring the three-body recombination rate in an ultracold gas of Cs atoms. In three dimensions, we measure the dependence of g(3) on the gas parameter in a BEC, finding good agreement with the theoretical prediction accounting for beyond-mean-field effects. In one dimension, we observe a reduction of g(3) by several orders of magnitude upon increasing interactions from the weakly interacting BEC to the strongly interacting Tonks-Girardeau regime, in good agreement with predictions from the Lieb-Liniger model for all strengths of interaction.

arXiv:1107.4516•Physical Review Letters•Dec 2, 2011•86 citations

Connection between nonlocal one-body and local three-body correlations of the Lieb-Liniger model

Maxim Olshanii, Vanja Dunjko, Anna Minguzzi +1 more

We derive a connection between the fourth coefficient of the short-distance Taylor expansion of the one-body correlation function, and the local three-body correlation function of the Lieb-Liniger model of $\ensuremath{\delta}$-interacting spinless bosons in one dimension. This connection, valid at arbitrary interaction strength, involves the fourth moment of the density of quasimomenta. Generalizing recent conjectures, we propose approximate analytical expressions for the fourth coefficient covering the whole range of repulsive interactions, validated by comparison with accurate numerics. In particular, we find that the fourth coefficient changes sign at interaction strength ${\ensuremath{\gamma}}_{c}\ensuremath{\simeq}3.816$, while the first three coefficients of the Taylor expansion of the one-body correlation function retain the same sign throughout the whole range of interaction strengths.

arXiv:1705.02100•Physical Review A•Sep 19, 2017•22 citations

Local correlations in a strongly interacting one-dimensional Bose gas

Dimitri M. Gangardt, Gora V. Shlyapnikov

We develop an analytical method for calculating local correlations in strongly interacting 1D Bose gases, based on the exactly solvable Lieb-Liniger model. The results are obtained at zero and finite temperatures. They describe the interaction-induced reduction of local many-body correlation functions and can be used for achieving and identifying the strong-coupling Tonks-Girardeau regime in experiments with cold Bose gases in the 1D regime.

arXiv:cond-mat/0304159•New Journal of Physics•Jun 18, 2003•86 citations

Exact results for three-body correlations in a degenerate one-dimensional Bose gas

Vadim Cheianov, H. Smith, Mikhail B. Zvonarev

Motivated by recent experiments we derive an exact expression for the correlation function entering the three-body recombination rate for a one-dimensional gas of interacting bosons. The answer, given in terms of two thermodynamic parameters of the Lieb-Liniger model, is valid for all values of the dimensionless coupling $\ensuremath{\gamma}$ and contains the previously known results for the Bogoliubov and Tonks-Girardeau regimes as limiting cases. We also investigate finite-size effects by calculating the correlation function for small systems of three, four, five, and six particles.

arXiv:cond-mat/0506609•Physical Review A•May 26, 2006•61 citations
We develop a method to calculate vacuum expectation values of local operators in the Lieb–Liniger model. This method is based on a set of new identities obtained using integrability and effective theory ('bosonization') description. We use this method to get an explicit expression for the three-body local correlation function, measured in a recent experiment.
The ground-state correlation functions of a one-dimensional homogeneous Bose system described by the Lieb-Liniger Hamiltonian are investigated by using exact quantum Monte Carlo techniques. This article is an extension of a previous study published in Phys. Rev. A {\bf 68}, 031602 (2003). New results on the local three-body correlator as a function of the interaction strength are included and compared with the measured value from three-body loss experiments. We also carry out a thorough study of the short- and long-range behavior of the one-body density matrix.
We investigate local three-body correlations for bosonic particles in three dimensions and one dimension as a function of the interaction strength. The three-body correlation function g(3) is determined by measuring the three-body recombination rate in an ultracold gas of Cs atoms. In three dimensions, we measure the dependence of g(3) on the gas parameter in a BEC, finding good agreement with the theoretical prediction accounting for beyond-mean-field effects. In one dimension, we observe a reduction of g(3) by several orders of magnitude upon increasing interactions from the weakly interacting BEC to the strongly interacting Tonks-Girardeau regime, in good agreement with predictions from the Lieb-Liniger model for all strengths of interaction.
We derive a connection between the fourth coefficient of the short-distance Taylor expansion of the one-body correlation function, and the local three-body correlation function of the Lieb-Liniger model of $\ensuremath{\delta}$-interacting spinless bosons in one dimension. This connection, valid at arbitrary interaction strength, involves the fourth moment of the density of quasimomenta. Generalizing recent conjectures, we propose approximate analytical expressions for the fourth coefficient covering the whole range of repulsive interactions, validated by comparison with accurate numerics. In particular, we find that the fourth coefficient changes sign at interaction strength ${\ensuremath{\gamma}}_{c}\ensuremath{\simeq}3.816$, while the first three coefficients of the Taylor expansion of the one-body correlation function retain the same sign throughout the whole range of interaction strengths.
Motivated by recent experiments we derive an exact expression for the correlation function entering the three-body recombination rate for a one-dimensional gas of interacting bosons. The answer, given in terms of two thermodynamic parameters of the Lieb-Liniger model, is valid for all values of the dimensionless coupling $\ensuremath{\gamma}$ and contains the previously known results for the Bogoliubov and Tonks-Girardeau regimes as limiting cases. We also investigate finite-size effects by calculating the correlation function for small systems of three, four, five, and six particles.