Ground-state Bethe root densities and quantum phase transitions

Links, Jon and Marquette, Ian (2015) Ground-state Bethe root densities and quantum phase transitions. Journal of Physics A: Mathematical and Theoretical, 48 4: 1-15. doi:10.1088/1751-8113/48/4/045204

Author Links, Jon
Marquette, Ian
Title Ground-state Bethe root densities and quantum phase transitions
Journal name Journal of Physics A: Mathematical and Theoretical   Check publisher's open access policy
ISSN 1751-8113
Publication date 2015-01
Year available 2015
Sub-type Article (original research)
DOI 10.1088/1751-8113/48/4/045204
Open Access Status
Volume 48
Issue 4
Start page 1
End page 15
Total pages 15
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2016
Language eng
Abstract Exactly solvable models provide a unique method, via qualitative changes in the distribution of the ground-state roots of the Bethe ansatz equations, to identify quantum phase transitions. Here we expand on this approach, in a quantitative manner, for two models of Bose–Einstein condensates. The first model deals with the interconversion of bosonic atoms and molecules. The second is the two-site Bose–Hubbard model, widely used to describe tunneling phenomena in Bose–Einstein condensates. For these systems we calculate the ground-state root density. This facilitates the determination of analytic forms for the ground-state energy, and associated correlation functions through the Hellmann–Feynman theorem. These calculations provide a clear identification of the quantum phase transition in each model. For the first model we obtain an expression for the molecular fraction expectation value. For the two-site Bose–Hubbard model we find that there is a simple characterization of condensate fragmentation.
Keyword Bethe ansatz
Quantum phase transition
Exacly solvable models
Bose-Einstein condensate
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
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Citation counts: TR Web of Science Citation Count  Cited 5 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 5 times in Scopus Article | Citations
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