The Lieb–Liniger model
Abstract
The Lieb–Liniger model describes one-dimensional bosons with contact interactions. This many-body system admits an exact solution in terms of the Bethe ansatz. Some of the exact and perturbative results for this model are reviewed. Particular attention is devoted to the explicit evaluation, in terms of the interaction parameter, of physical quantities that can be formally exactly extracted from the Bethe ansatz solution. Another goal of this review is to stress exact relations between various quantities. The technical developments are explained in detail. The most relevant experimental realisations of the studied problems are eventually discussed. This review also contains several new results such as the study of convergence of the ground-state energy series at strong interactions, the excitation spectrum at high energies, and the evaluation of the boundary energy.
Related
- Asymptotic analysis of a Fredholm determinant occurring in the description of the dynamical correlation functions of the Lieb--Liniger Bose gas
- Emergence of nonequilibrium Lieb excitations in periodically-driven strongly-interacting bosons
- Lieb-Robinson bounds via the Combes-Thomas estimate
- Lieb-Robinson bounds for irreversible dynamics via adaptive Dyson expansion
- Field-driven quantum phase transitions in a spin-1/2 Heisenberg antiferromagnet on an extended Lieb lattice
BibTeX
@article{ristivojevic2026liebliniger,
title = {{The Lieb–Liniger model}},
author = {Zoran Ristivojevic},
journal = {Journal of Physics A: Mathematical and Theoretical},
year = {2026},
month = sep,
doi = {10.1088/1751-8121/ae6428},
eprint = {2604.24784},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05847434v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - The Lieb–Liniger model
AU - Zoran Ristivojevic
PY - 2026
DA - 2026/09/16
JO - Journal of Physics A: Mathematical and Theoretical
DO - 10.1088/1751-8121/ae6428
UR - https://hal.science/hal-05847434v1
AB - The Lieb–Liniger model describes one-dimensional bosons with contact interactions. This many-body system admits an exact solution in terms of the Bethe ansatz. Some of the exact and perturbative results for this model are reviewed. Particular attention is devoted to the explicit evaluation, in terms of the interaction parameter, of physical quantities that can be formally exactly extracted from the Bethe ansatz solution. Another goal of this review is to stress exact relations between various quantities. The technical developments are explained in detail. The most relevant experimental realisations of the studied problems are eventually discussed. This review also contains several new results such as the study of convergence of the ground-state energy series at strong interactions, the excitation spectrum at high energies, and the evaluation of the boundary energy.
SN - 1751-8113
SN - 1751-8121
ER -