dorsal/arxiv
View SchemaOn quantum phase crossovers in finite systems
| Authors | Clare Dunning, Katrina E. Hibberd, Jon Links |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602098 |
| URL | https://arxiv.org/abs/quant-ph/0602098 |
| DOI | 10.1088/1742-5468/2006/11/P11005 |
| Journal | J Stat Mech: Theor. Exp. (2006) P11005 |
Abstract
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 Schr\"odinger operator. Bifurcations of the minima for the potential of the Schr\"odinger 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.
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"abstract": "In this work we define a formal notion of a quantum phase crossover for\ncertain Bethe ansatz solvable models. The approach we adopt exploits an exact\nmapping of the spectrum of a many-body integrable system, which admits an exact\nBethe ansatz solution, into the quasi-exactly solvable spectrum of a one-body\nSchr\\\"odinger operator. Bifurcations of the minima for the potential of the\nSchr\\\"odinger operator determine the crossover couplings. By considering the\nbehaviour of particular ground-state correlation functions, these may be\nidentified as quantum phase crossovers in the many-body integrable system with\nfinite particle number. In this approach the existence of the quantum phase\ncrossover is not dependent on the existence of a thermodynamic limit, rendering\napplications to finite systems feasible. We study two examples of bosonic\nHamiltonians which admit second-order crossovers.",
"arxiv_id": "quant-ph/0602098",
"authors": [
"Clare Dunning",
"Katrina E. Hibberd",
"Jon Links"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1742-5468/2006/11/P11005",
"journal_ref": "J Stat Mech: Theor. Exp. (2006) P11005",
"title": "On quantum phase crossovers in finite systems",
"url": "https://arxiv.org/abs/quant-ph/0602098"
},
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