On the reality of spectra of Uq(sl2)-invariant XXZ Hamiltonians

Morin-Duchesne, Alexi, Rasmussen, Jorgen, Ruelle, Philippe and Saint-Aubin, Yvan (2016) On the reality of spectra of Uq(sl2)-invariant XXZ Hamiltonians. Journal of Statistical Mechanics: Theory and Experiment, 2016 5: . doi:10.1088/1742-5468/2016/05/053105


Author Morin-Duchesne, Alexi
Rasmussen, Jorgen
Ruelle, Philippe
Saint-Aubin, Yvan
Title On the reality of spectra of Uq(sl2)-invariant XXZ Hamiltonians
Formatted title
On the reality of spectra of Uq(sl2)-invariant XXZ Hamiltonians
Journal name Journal of Statistical Mechanics: Theory and Experiment   Check publisher's open access policy
ISSN 1742-5468
Publication date 2016-05-11
Year available 2016
Sub-type Article (original research)
DOI 10.1088/1742-5468/2016/05/053105
Open Access Status Not yet assessed
Volume 2016
Issue 5
Total pages 35
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2017
Language eng
Formatted abstract
A new inner product is constructed on each standard module over the TemperleyLieb algebra TLn (β) for β ϵ R and n ≥ 2. On these modules, the Hamiltonian h = ∑i ei is shown to be self-adjoint with respect to this inner product. This implies that its action on these modules is diagonalisable with real eigenvalues. A representation theoretic argument shows that the reality of spectra of the Hamiltonian extends to all other TemperleyLieb representations. In particular, this result applies to the celebrated Uq(sl2)-invariant XXZ Hamiltonian, for all q + q-1ϵ R.
Keyword Algebraic structures of integrable models
Integrable spin chains (vertex models)
Loop models and polymers
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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