|
Statut |
Confirmé |
|
Série |
SEM-EXCEP , SEM-INFOR |
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Domaines |
cond-mat |
|
Date |
Vendredi 26 Octobre 2018 |
|
Heure |
11:30 |
|
Institut |
LPTENS |
|
Salle |
LPTENS Library |
|
Nom de l'orateur |
Lajko |
|
Prenom de l'orateur |
Miklos |
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Addresse email de l'orateur |
|
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Institution de l'orateur |
EPFL Lausanne |
|
Titre |
Generalization of the Haldane conjecture to SU(3) chains |
|
Résumé |
About 35 years ago, Haldane's conjecture for Heisenberg spin chains came as a surprise to both the
condensed matter and high energy physics communities. Mapping the low energy degrees of freedom of a
spin chain in the large-S limit to the 1+1 dimensional O(3) nonlinear sigma model with a nontrivial topological
term, Haldane argued that integer and half-integer chains have qualitatively different behaviours: while half-
integer spin chains are gapless, integer spin chains are gapped with a unique ground state.
In my talk I will give a short review of Haldane's argument, then I will explain how it can be extended to SU(3)
chains in the fully symmetric representation with p boxes in the Young tableau. In this case the low energy
degrees of freedom can be mapped into a SU(3)/(U(1) x U(1)) nonlinear sigma model with a topological angle
$\theta =2\pi p/3$. I will analyse the phase diagram of this nonlinear sigma model using symmetry
considerations and analytic calculations in the strong coupling limit, complemented by Monte Carlo
simulations on lattice systems. I will discuss the relation between the sigma model and the spin chain system
arguing that SU(3) spin chains are gapped for $p=3m$ but gapless for $p=3m\pm 1$ (for integer $m$),
corresponding to a massless critical point of the sigma model at $\theta =\pm 2\pi /3$. |
|
Numéro de preprint arXiv |
1706.06598 |
|
Commentaires |
Ref. ML, Kyle Wamer, Frederic Mila, Ian Affleck, Nuclear Physics B 924, 508 (2017) |
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Fichiers attachés |
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