Chain of interacting $SU(2)_4$ anyons and quantum $SU(2)_k\times\overline{SU(2)_k}$ doubles
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 514-528
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We consider a chain of $SU(2)_4$ anyons with transitions to a topologically ordered phase state. For half-integer and integer indices of the type of strongly correlated excitations, we find an effective low-energy Hamiltonian that is an analogue of the standard Heisenberg Hamiltonian for quantum magnets. We describe the properties of the Hilbert spaces of the system eigenstates. For the Drinfeld quantum $SU(2)_k
\times\overline{SU(2)_k}$ doubles, we use numerical computations to show that the largest eigenvalues of the adjacency matrix for graphs that are extended Dynkin diagrams coincide with the total quantum dimensions for the levels $k=2,3,4,5$. We also formulate a hypothesis about the reason for the universal behavior of the system in the long-wave limit.
Keywords:
modular tensor category, quantum double, anyon.
@article{TMF_2011_167_3_a14,
author = {V. A. Verbus and L. Martina and A. P. Protogenov},
title = {Chain of interacting $SU(2)_4$ anyons and quantum $SU(2)_k\times\overline{SU(2)_k}$ doubles},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {514--528},
publisher = {mathdoc},
volume = {167},
number = {3},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a14/}
}
TY - JOUR
AU - V. A. Verbus
AU - L. Martina
AU - A. P. Protogenov
TI - Chain of interacting $SU(2)_4$ anyons and quantum $SU(2)_k\times\overline{SU(2)_k}$ doubles
JO - Teoretičeskaâ i matematičeskaâ fizika
PY - 2011
SP - 514
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VL - 167
IS - 3
PB - mathdoc
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V. A. Verbus; L. Martina; A. P. Protogenov. Chain of interacting $SU(2)_4$ anyons and quantum $SU(2)_k\times\overline{SU(2)_k}$ doubles. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 514-528. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a14/