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On quantum phase crossovers in finite systems

Hibberd, Katrina E., Dunning, Clare, Links, Jon (2006) On quantum phase crossovers in finite systems. Journal of Statistical Mechanics: Theory and Experiment, (P11005). p. 11. ISSN 1742-5468. (doi:10.1088/1742-5468/2006/11/P11005) (KAR id:4712)

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In this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe ansatz solution, into the quasi-exactly solvable spectrum of a one-body Schrodinger operator. Bifurcations of the minima for the potential of the Schrodinger operator determine the crossover couplings. By considering the behaviour of particular ground state correlation functions, these may be identified as quantum phase crossovers in the many-body integrable system with finite particle number. In this approach the existence of the quantum phase crossover is not dependent on the existence of a thermodynamic limit, rendering applications to finite systems feasible. We study two examples of bosonic Hamiltonians which admit second-order crossovers.

Item Type: Article
DOI/Identification number: 10.1088/1742-5468/2006/11/P11005
Uncontrolled keywords: quantum integrability (Bethe ansatz) Bose Einstein condensation (theory) BETHE-ANSATZ EQUATIONS BEHAVIOR
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Clare Dunning
Date Deposited: 01 Sep 2008 13:51 UTC
Last Modified: 06 May 2020 03:01 UTC
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