LOCALIZED ENDOMORPHISMS IN KITAEV'S TORIC CODE ON THE PLANE
2011 ◽
Vol 23
(04)
◽
pp. 347-373
◽
Keyword(s):
We consider various aspects of Kitaev's toric code model on a plane in the C*-algebraic approach to quantum spin systems on a lattice. In particular, we show that elementary excitations of the ground state can be described by localized endomorphisms of the observable algebra. The structure of these endomorphisms is analyzed in the spirit of the Doplicher–Haag–Roberts program (specifically, through its generalization to infinite regions as considered by Buchholz and Fredenhagen). Most notably, the statistics of excitations can be calculated in this way. The excitations can equivalently be described by the representation theory of [Formula: see text], i.e. Drinfel'd's quantum double of the group algebra of ℤ2.
1983 ◽
Vol 16
(25)
◽
pp. L913-L918
◽
Keyword(s):
Cusp singularity in the magnetization curve of quantum spin systems with a dimer-gapped ground state
2003 ◽
Vol 329-333
◽
pp. 1277-1278
◽
Keyword(s):
2012 ◽
Vol 27
(01n03)
◽
pp. 1345030
◽
1989 ◽
Vol 58
(7)
◽
pp. 2607-2607
◽
1994 ◽
Vol 27
(4)
◽
pp. 1127-1138
◽
Keyword(s):
1988 ◽
Vol 57
(2)
◽
pp. 626-638
◽
1998 ◽
Vol 67
(1)
◽
pp. 5-7
◽
Keyword(s):