Exact Results for the Moments of the Rapidity Distribution in Galilean-Invariant Integrable Models

Autor:	Ristivojevic, Zoran
Rok vydání:	2022
Předmět:	Condensed Matter - Statistical Mechanics Condensed Matter - Quantum Gases Mathematical Physics
Zdroj:	Phys. Rev. Lett. 130, 020401 (2023)
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevLett.130.020401
Popis:	We study a class of Galilean-invariant one-dimensional Bethe ansatz solvable models in the thermodynamic limit. Their rapidity distribution obeys an integral equation with a difference kernel over a finite interval, which does not admit a closed-form solution. We develop a general formalism enabling one to study the moments of the rapidity distribution, showing that they satisfy a difference-differential equation. The derived equation is explicitly analyzed in the case of the Lieb-Liniger model and the moments are analytically calculated. In addition, we obtained the exact information about the ground-state energy at weak repulsion. The obtained results directly enter a number of physically relevant quantities. Comment: 6 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.07481 Zobrazit plný text záznamu View this record from Arxiv