Quantum Information Meets Quantum Matter by Bei Zeng & Xie Chen & Duan-Lu Zhou & Xiao-Gang Wen

Author:Bei Zeng & Xie Chen & Duan-Lu Zhou & Xiao-Gang Wen
Language: eng
Format: epub
ISBN: 9781493990849
Publisher: Springer New York

(6.17)

From Fig. 6.20, we see that, starting from a two-particle state with the two particles at site-a and site-d, there are two ways to move the two particles to site-b and site-c. The two ways of hopping differ by an exchange of the two particles. Therefore, the statistics of the particle can be determined by the algebra of the hopping operators. If the hopping operator satisfies

(6.18)

then the statistics of the particle is given by .

So, to calculate the statistics of e, we need to know the algebra of the hopping operator for e. This can be easily done since the hopping operator for e is nothing but the type-I open string operator that connects the site-i and site-j. Therefore, the algebra of the open string operator determine the statistics of the string ends.

Fig. 6.20There are two ways to move a two-particle state (with the two particles at site-a and site-d) to another two-particle state (with the two particles at site-b and site-c). The ways differ by an exchange of the two particles

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