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Symmetry fractional quantization in two dimensions | Hong Yao
; Liang Fu
; Xiao-Liang Qi
; | Date: |
20 Dec 2010 | Abstract: | We introduce a solvable spin-rotational and time-reversal invariant spin-1
model in two dimensions. Depending on parameters, the ground state is an
equal-weight superposition of all valence loops called "resonating valence
loop" (RVL) or an equal-weight superposition of all valence bonds known as
"resonating valence bond" (RVB). In RVL, ends of open loops are deconfined
spinons of spin-1/2 that cannot be obtained by simple combinations of spin-1 --
a phenomenon of fractionalization; while in RVB, all quasiparticles carry an
integer spin, hence no fractionalization. RVL and RVB are spin liquids with
identical topological order but different spin-rotational and time-reversal
symmetry quantum numbers of quasiparticles. We propose that quantized symmetry
quantum number gives a systematic way to (partially) classify phases with
identical topological order in dimensions greater than one. | Source: | arXiv, 1012.4470 | Services: | Forum | Review | PDF | Favorites |
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