# Low-density limit of dynamical correlations in the Lieb–Liniger model

@article{Granet2020LowdensityLO, title={Low-density limit of dynamical correlations in the Lieb–Liniger model}, author={Etienne Granet}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2020}, volume={54} }

We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb–Liniger model, within an arbitrary eigenstate with a small particle density D . They are valid for all space and time and any interaction strength c > 0, and are the leading order of an expansion in D . This expansion is obtained by writing the correlation functions as sums over form factors when formally decomposed into partial fractions.

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## References

SHOWING 1-10 OF 86 REFERENCES

Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium

- Physics
- 2016

We study the density-density correlation function of the 1D Lieb-Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We…

Finite-temperature correlations in the Lieb-Liniger one-dimensional Bose gas

- Physics
- 2014

We address the problem of calculating finite-temperature response functions of an experimentally relevant low-dimensional, strongly correlated system: the integrable one-dimensional Bose gas with a…

Density form factors of the 1D Bose gas for finite entropy states

- Physics
- 2014

We consider the Lieb–Liniger model for a gas of bosonic δ-interacting particles. Using Algebraic Bethe Ansatz results we compute the thermodynamic limit of the form factors of the density operator…

One-particle dynamical correlations in the one-dimensional Bose gas

- Physics, Mathematics
- 2007

The momentum- and frequency-dependent one-body correlation function of the one-dimensional interacting Bose gas (Lieb–Liniger model) in the repulsive regime is studied using the Algebraic Bethe…

Particle-hole pairs and density–density correlations in the Lieb–Liniger model

- Physics
- 2017

We review the recently introduced thermodynamic form factors for pairs of particle-hole excitations on finite-entropy states in the Lieb–Liniger model. We focus on the density operator and we show…

Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas

- Physics
- 2010

We describe a Bethe ansatz-based method to derive, starting from a multiple integral representation, the long-distance asymptotic behavior at finite temperature of the density–density correlation…

A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model

- Physics
- 2020

We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a…

Correlation lengths of the repulsive one-dimensional Bose gas

- Physics
- 2013

We investigate the large-distance asymptotic behavior of the static density-density and field-field correlation functions in the one-dimensional Bose gas at finite temperature. The asymptotic…

Correlation functions for one-dimensional bosons at low temperature

- Physics
- 2011

We consider the low-temperature limit of the long-distance asymptotic behavior of the finite-temperature density–density correlation function in the one-dimensional Bose gas derived recently in the…

Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions

- Physics
- 2009

We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply…